Although there is good evidence that rivers and even lakes temporarily existed on the Mars when that planet was much younger, astronomers are still debating whether a temporary ocean ever existed in a large depression in the northern plains. Two scientists discuss the evidence for an ocean.

Scientist 1

Satellite data show a feature that resembles some of the shorelines surrounding Earth’s oceans: a terrace, “Shoreline A,” that is almost always at the same elevation wherever it is visible.  There are also three more features that resemble features found in some of Earth’s oceans:

First, there is some evidence for additional terraces at other elevations (representing earlier or later times when the sea level was at that higher or lower elevation for a long period of time).

Second, the surface is much smoother inside Shoreline A than outside the shoreline, exactly as is the case in Earth’s present oceans.

Third, there are features resembling river channels leading into the depression.

Scientist 2

In a few locations (near the Tharsis and Elysium volcanoes, and also near the Lyot crater), the elevation of the proposed Shoreline A is much higher than elsewhere.  The situation is much worse for some of the other potential shorelines – The largest, “Shoreline B,” obviously cannot correspond to the boundary of an ancient ocean because its elevation varies by several kilometers from one end to the other.  The surface of any body of water will, of course, be level – so its shore must also be at the same height at every point.

Even without looking at the questions yet, we can see there is a lot of tiny detail here! Don’t feel the need to understand everything. The question will tell us where to look for the correct answer. Now let’s look at one:

Question 1:  According to the passage, an ocean must have:

A                  A surface that is at the same elevation at all points

B                  A bottom that is at the same elevations at all points

C                  A depth that is the same at different points

D                  A depth that is different at different points

Ask yourself: where was ocean requirements discussed? Scientist 2 talked about why something couldn’t be a shoreline, so let’s look back to that paragraph and search for the criteria he used to draw his conclusion. As Scientist B stated, the surface of any body of water (including an ocean) must be level. He said Shoreline B couldn’t correspond because of the specific detail, “elevation varies.” A level surface is a surface whose elevation is the same at all points. The answer to this Details question is A.

Here’s another ACT science question for more practice. Good luck!

Try this ACT math question for practice!

Perimeter

The perimeter is the distance around any shape. For a triangle, the perimeter will be the sum of the sides. For a rectangle, the formula is P = l + l + w + w, or P = 2l + 2w. For a square, this becomes P = 4s. For other quadrilaterals, you need to know the length of each side in order to find the perimeter, unless you are given more information about the comparative lengths of the sides.

For a circle, the perimeter is equal to the circumference: C = 2πr.

Area

Triangles – To find the area of a triangle, we use the formula A = ½ bh, where b = base and h = height. The base and the height of the triangle must always form a 90 degree angle. Keep in mind that the height can be inside or outside the triangle.

Quadrilaterals – To find the area of a square, we use the formula A = s², where s = side of the square.

To find the area of a rectangle, we use the formula A = lw, where l = length and w = width.

To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. We do NOT simply multiply the two side lengths. Remember the base and the height must be perpendicular.

To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. We essentially take the average of the two bases, and multiply it by the height. Again, the height is perpendicular to each base.

Polygons – To find the area of figures with MORE than four sides, the key is to break up the figure into smaller parts.

Circles – To find the area of a circle, use the formula A = πr².

Volume

The volume of a solid is the amount of space enclosed by that solid. The volume of any solid is always equal to the area of the base multiplied times the height.

The volume of a rectangular solid, therefore, is V = lwh. The volume of a cube (with six equal sides) is V = s³. The volume of a cylinder (a solid whose cross-section is a circle) is found using the formula V = πr²h.

Ready to get started applying these formulas? Check out any of the Group Games in the ACT Grockit Lobby. You can even create a custom game for yourself with only those concepts you’d like to study by clicking “Create Game.” Don’t forget to contact any of Grockit’s ACT Tutors if you have any questions or would like to set up a Tutoring lesson!

Try this ACT science question for practice today!

Geologists describe the orientation of sedimentary rock layers using two angles, “dip” and “strike.”  The dip indicates how far from horizontal the rock layer is tilted, and the strike indicates the compass direction along which the rock layer has been tilted.  For example, a dip of 1 degree indicates that a rock layer is nearly horizontal – it slopes downward at an angle of only 1 degree.  A strike of 1 degree indicates that the rock layer is tilted along a line running 1 degree east of north (i.e. almost due north), a strike of 90 degrees indicates that the rock layer is tilted along a line running 90 degrees east of north (i.e. due east), and so forth.

Within a mountain range, strike values are typically similar.  For instance, a map will show that the Allegheny Mountains run from southwest to northeast, and the strikes of rock layers within this area are often approximately the same (a value of approximately 45 degrees, corresponding to northeast).  In addition, near the outer edge of a mountain range, rock layers will generally be tilted much less than near the center of the range. Table 1 shows the dips and strikes measured at several points in a square mile of the Allegheny Mountains.

Figures 1 and 2 show how the average dip and average strike vary at 25-mile intervals along a particular north-south line in the Alleghenies.

Question 1: According to Figure 1, from north to south, the average dip:

A                  increases only

B                  decreases only

C                  decreases, then increases

D                  increases, then decreases

We can tell this is a Physical Sciences passage because it deals with Geology. Even if we don’t know anything about Geology, we can still use the presented data to get the question correct. The label at the bottom of the figure indicates that the northernmost point is plotted at the left edge of the graph, and the southernmost point at the right edge. Thus, the question asks how the average dip changes from left to right. It can be seen that the dip increases from slightly over 10 degrees to slightly over 40 degrees, then decreases again to slightly over 30 degrees. The answer is D.

Question 2: Which of the following describes a rock layer that is tilted vertically along a line running northeast?

A                  dip = 45 degrees, strike = 90 degrees

B                  dip = 90 degrees, strike = 45 degrees

C                  dip = 180 degrees, strike = 90 degrees

D                  dip = 180 degrees, strike = 45 degrees

A dip of 1 degree indicates that the rock layer is tipped 1 degree from the horizontal. We need to know the dip that corresponds to tilting the rock layer until it is vertical. If we draw a picture of this situation, we see that the vertical line and the horizontal line make an angle of 90 degrees, so the dip is 90 degrees when the bed is tilted vertically. A strike of 1 degree indicates that the rock layer is tilted along a line running 1 degree east of due north, so a strike of 45 degrees indicates that the rock layer is tilted along a line 45 degrees east of due north, or northeast. This is confirmed by the discussion of the Allegheny Mountains, in which the typical strike of 45 degrees matches the orientation of the mountain range, which runs northeast. The answer is B.

For more practice with Physical Science passages, create a Custom Game in Grockit’s ACT lobby; use “Physical Science” as your skill tag. For even more help, schedule a 1-hour tutoring lesson with any of Grockit’s ACT Tutors. Check out the “Tutoring” tab in the ACT Grockit lobby for more info!

Let’s look at an example Conflicting Viewpoints passage from Grockit’s question bank to start practicing for the ACT right now!

The velocity with which a small body A orbits a much more massive body B depends on the mass of body B and the distance between the two bodies: If body B is twice as massive, body A will orbit it at twice the velocity, and if body B is more distant from body A, it will orbit more slowly.

These relationships allow astronomers to predict the velocities at which stars in a galaxy should orbit the center of the galaxy, based on the total mass of the visible stars.  In certain cases, however, the measured velocities of the stars in a galaxy are greater than predicted.  This indicates that the galaxy must contain additional material (often termed “dark matter”) which astronomers are unable to see.

Figure 1 shows how dark the presence of dark matter alters the velocities of the stars in a hypothetical galaxy:  The lower “no dark matter” curve shows the theoretical velocities in a galaxy containing 100 million stars similar to the Sun in a sphere 5 kiloparsecs (kpc) in radius, and the upper “dark matter” curve shows the theoretical velocities if the stars are embedded in the center of a dark matter cloud that is much larger and much more massive than the visible galaxy.

Study 1

Astronomers have measured the velocities of stars in the galaxy NGC 3198.  The results are shown in Figure 2.  The “no dark matter” model in Figure 1 would have predicted a decline in the velocities at distances greater than the 5 kpc radius of the galaxy, but instead they remain approximately constant.

Study 2

Astronomers have measured the velocities of stars in 100 additional galaxies of approximately the same size (diameter and mass) as NGC 3198.  The velocities of the stars are approximately the same as in NGC 3198.

Question 1: Which of the following statements correctly describes a possible reason why many additional galaxies were examined in Study 2?

A                  To determine whether they showed the same evidence of dark matter as NGC 3198.

B                  To determine the theoretical relationship between velocity and distance from the center of the galaxy

C                  To confirm that the velocities of the stars in these galaxies also match the theoretical “no dark matter” predictions

D                  To determine whether the same velocity changes occur in much larger galaxies

We know this is an Assumption question because of the phrase “a possible reason.” Think back to the passage – what is a logical basis for the set-up of Study 2? Notice how Figure 1 shows that the theoretical curves for the “no dark matter” and “dark matter” cases differ greatly. The experimental observations for the NGC 3198 galaxy, shown in Figure 2, obviously match the shape of the theoretical “dark matter” curve and obviously do not match the shape of the theoretical “no dark matter” curve. This is clear evidence for the presence of dark matter in this particular galaxy, and a study of other galaxies with similar characteristics using the same technique could indicate whether dark matter is a typical feature of such galaxies. The answer is A.

Question 2: Which of the following statements can best explain why the velocities of the stars in NGC 3198, as shown in Figure 2, are different from the velocities of the stars in the hypothetical galaxy in Figure 1?

A                  The stars in NGC 3198 have higher velocities because the mass of NGC 3198 is larger

B                  The stars in NGC 3198 have higher velocities because the mass of NGC 3198 is smaller

C                  The stars in NGC 3198 have lower velocities because the mass of NGC 3198 is larger

D                  The stars in NGC 3198 have lower velocities because the mass of NGC 3198 is smaller

Again, we know we are being asked about an unspoken assumption because of the phrase “best explain why.” Here we have to “see through” to the core  of what the data actually means. Select any distance from the center of the galaxy, and compare Figures 1 and 2 at that distance. The velocity in Figure 2 (NGC 3198) will be higher than the value on either curve in Figure 1 (the hypothetical galaxy) so only answers A or B can be correct. The passage notes that the velocity of an orbiting body is higher when the mass of the body it orbits is greater. Thus, the higher velocities in NGC 3198 can be explained if the mass of NGC 3198 is larger. The answer is A.

Been on your Grockit profile lately? You’ll notice all of your ACT percentages adjust with each question you answer. Use your personalized skill data to get a sense of your strengths and weaknesses and direct you what to study next in your Solo Practice!

Find more great ACT science advice here!

A prediction is an inference you make based on the given information. You will ALWAYS need to understand the given information first, before you can use it as the basis for your prediction. Sometimes all you will need to do is to carefully interpret the data to answer the question, like in this example from Grockit’s question bank:

The pitch of the sound made by rustling leaves is most similar to that of:

A     a shout

B    heavy street traffic

C   a whisper

D   thunder

Notice how the pitch of rustling leaves has a relatively small range, between 1 and 10,000 Hz. Heavy street traffic, thunder, and a whisper both have a too broad range. The answer is (A). Sometimes to make a prediction you will have to extend the information given to you by the passage:

Based on Figure 2, the oxygen saturation of Individual 2 at an altitude of 7 miles would be closest to:

A   0%

B   30%

C   60%

D   90%

The altitude in the question, 7 miles, is 1 mile higher than the highest data point shown in Figure 2 so this means we will have to make our own prediction.  We can do this by extrapolating the line that would be formed by connecting the “Individual 2″ data points. From 4 miles to 6 miles this line drops from approximately 80% to approximately 50% – a drop of 30% as the altitude increases by 2 miles.       Extending the line, a further increase of 1 mile (half of 2 miles) in altitude would result in a further drop of 15% (half of 30%) in saturation. The final saturation would equal 50% minus 15%, or 35%. This is closest to answer B, 30%.

This question asked you to make a prediction for a given variable based on extending a graph. Another question might ask you to make a prediction for an entirely new variable but based on the current trends:

If a third protein had been present, with a molecular weight of 13,400 Daltons, its elution time would have been approximately:

A   21 minutes

B   22 minutes

C   23 minutes

D   24 minutes

The key phrase here “if a third protein had been present” indicates that we will need to make a prediction for an entirely new situation based on the info they’ve given me. The molecular weight of the protein (13,400) lies between the weights of the two proteins in Table 1 (12,000 and 15,000). The time required for it to travel through the column will therefore be between the time required for the first protein (24 minutes) and the second protein (22 minutes). The weight lies approximately midway between the weights of the two proteins in the table, so its elution time will be close to midway between 24 and 22 minutes. The best estimate is 23 minutes, or choice C.

Get more practice with ACT Science by taking a free diagnostic on Grockit today! Click on “Study Plan” on your personal homepage and Grockit will direct you where to focus your studies!

Find out how you can track your progress across specific skills and target your efforts for ACT science on Grockit.

1. Pause to read the labels. Lots of students ignore the labels and go straight to the questions – don’t! Mentally categorize each graph, chart and table. (EX: “This is a chart that shows the relationship between time and distance for various lightwaves.”) Do not just skip the statistics entirely and go straight to the question! While you may think this will save you time, it actually significantly decreases your accuracy. Data Analysis questions are like an open-book test. You wouldn’t skip an ACT Reading passage, so don’t skip the data. Make sure you read every tiny piece of writing on or near the data, including titles, the labels for the x and y-axes, column names, and even footnotes.
2. Check out the units. Once you understand the labels, take special care to note the units (mph, m/sec, cm², etc.). Are we dealing with seconds, minutes, or hours? Does one graph represent the month of June, while the other graph represents the entire year? The units may change from graph-to-graph or chart-to-table, and some ACT Science questions might ask you do simply conversions.
3. Look for direct/inverse variation. Quickly note the relationship between the variables in each table, chart, or graph. Do they have a direct or indirect correlation? Where does the data spike or significantly decrease?
4. Treat the passage like an open-book test. One of the most common mistakes on the ACT Science Test is using the wrong data. You don’t have to rush to answer. The data you need IS in the passage, you just have to know where to look. Make sure you first understand what the question is asking, then stop and consider which table, graph, or chart provides the information you’ll need to solve for the correct answer. Harder ACT Science questions will require you to use more than one statistic. Don’t rush through this step! The questions may be multi-step, so look closely for key phrases in the question that refer to the labels you carefully studied earlier.
5. Approximate when needed. You may be able to approximate an answer by rounding off numbers for certain questions. Make sure to be consistent in how you approximate, and only do so if the answer choices are far enough apart that estimation makes sense.
6. Look for the general direction behind the reasoning. Most scientific reasoning either goes from broad to specific, or from specific to broad. It can be helpful in certain Conflicting Viewpoints questions whether the scientists are using a specific instance to make a generalization, or whether they are trying to apply a generalization to a specific rule.

Need more help with ACT practice test questions? Contact one of Grockit’s ACT tutors to set up a private tutoring lesson! Check out more info on the Tutoring tab in the Grockit lobby.

Try this ACT science question for practice!

A study of patients who have been taking the prescription drug rosiglitazone has raised doubts about this medicine’s safety.  Of the 6,241 patients who had taken the medicine for more than one year, 93 suffered heart attacks and 102 suffered heart failure.  By comparison, only 84 cases of heart attacks and 62 cases of heart failure were reported among the 7,870 patients in the control group (who had the same illness but did not receive rosiglitazone).

Scientist 1:

Based on the above results, the medicine appears to raise the risk of heart disease: 1 out of every 66 patients taking the medicine suffered heart attacks, versus only 1 in every 95 patients who were not taking the medicine.  The risk of heart failure increased even more.

The best course of action would therefore be to stop the sale of this medicine while a larger follow-up study is performed to confirm the results.

Scientist 2:

I agree that the results of the study are worrisome.  As Scientist 1 noted, approximately 1.5% of the patients taking rosiglitazone experienced heart attacks, compared to approximately 1.1% of the patients not taking this medicine.  However, such studies provide only an estimate of the true risks – and when the number of patients reporting a particular side effect is small, the estimates are likely to contain significant errors.

In this case, the differences between the two groups could be due to errors in the estimates.  For example, consider the fraction of patients taking rosiglitazone who suffer heart attacks, which is estimated to be 93 out of every 6,241. According to the laws of statistics, the uncertainty in this risk estimate can be estimated simply by taking the square root of 93, which is approximately 10.  There is actually 1 chance in 3 that the risk estimate is in error by more than this amount, so the true value could well be less than 83 out of every 6,241 (rather than 93).  It is equally possible that the correct number in the other group is more than 93 out of 7,870 (rather than 84).

A larger follow-up study should be performed as soon as possible, but I would not advise banning use of rosiglitazone in the meantime.  This medicine has been shown to be effective at preventing a dangerous illness, and patients would be harmed if they switch to a medicine that turns out to be less effective.

Question 1: According to Scientist 2, the accuracy of the risk estimates in such a study will:

A                  depend on the square of the number of patients

B                  depend on the number of patients

C                  depend on the square root of the number of patients

D                  not depend on the number of patients

In this passage, Scientist 2 emphasizes that large errors in the risk estimates can occur when the sample size is small (“when the number of patients…is small, the estimates are likely to contain significant error.) Scientist 2 then uses one estimate from the study as an example (paragraph 2), and explains that the square root of the number of patients (“can be estimated simply by taking the square root of 93….”) will indicate the possible error in the estimate. The answer is C.

Question 2: Assume that another study reported the following results: 62 of 6,550 patients taking rosiglitazone suffered heart attacks, and 107 suffered heart failure. 80 of 7,500 patients in the control group suffered heart attacks, and 59 suffered heart failure. Which of these results is least consistent with the results of the previous study?

A                  heart attacks among patients taking the medicine

B                  heart failure among patients taking the medicine

C                  heart attacks among patients not taking the medicine

D                  heart failure among patients not taking the medicine

The number of patients taking the medicine is 6,550, only a tiny amount more than the 6,241 patients taking the medicine in the original study. Similarly, the number of patients in the control group changed minimally, from 7,870 to 7,500. Therefore, the number of patients in a particular group who experience a particular side effect should be similar to the number in the original study. Only the number of heart attacks in the group taking the medicine changed by more than a few percent. This number was 62 in the new study, but it had been 93 – one and a half times as many – in the original study. The answer is A.

Learn more about how to approach Conflicting Viewpoints passages specifically by checking out this Grockit blog here.

Create an “Example Chart” like the one pictured below, and add at least 3 to each category. Choose things that you are an expert in, not ones that necessarily sound the most scholarly. You should know enough about each example so that you could write a detailed paragraph describing them. If you feel like adding 4 or 5 to a certain category, rather than just 3, then go for it! Not everyone will have a lot of ideas for “Science” or “Videogames.” You can even make your own category.

The idea is that by the time you arrive at your SAT Test Day, you will already have brainstormed a lot of possible examples. When you see the prompt in Section 1 of the SAT, you won’t waste valuable time coming up with examples. All you’ll have to ask yourself is: which examples from my Example Chart best match this specific prompt?

Try to match 3 different examples to each side of the prompt, and then choose to argue the position for which you have the best examples. You don’t even have to agree with that side! The reader won’t penalize you for your opinion – they just want to see a specific, forceful, well-reasoned essay.

Let’s look at an example SAT essay prompt:

Assignment: Do you believe that success is based more on natural talents and inherent abilities, or more on hard work?

The two sides of the issue are “YES, success is based on talent” or “NO, success is based on hard work.” If we wanted to choose the “YES” approach, we could pick three examples from our chart like: Grandma, Kanye West, and Career as a doctor. We could argue that something from our Grandma’s life shows she was successful based on talent. We could say that Kanye’s success is based on talent, and we could argue that to be successful as a medical field requires an inherent aptitude in science and physiology.

If we went the other direction, we could choose three examples to supports the “NO” position: Abraham Lincoln, Egyptian pyramids, and Twitter. We could argue that Lincoln was born in a log cabin but achieved the presidency based on hard work. We could say that the pyramids are emblematic of what human tenacity and ingenuity can achieve. Finally, we could say that the expansion of businesses into social media and Twitter shows that people know their hard work in promoting their businesses and career will actively pay off.

Once you create your Example Chart, apply your examples to multiple sample prompts. You may find that you go back to certain examples over and over again. Some are more “flexible” than others and depending on your argument, could actually be used to support either side of the prompt. Just make sure to always take a strong stand on the issue, and don’t take a 50/50 “middle of the road” approach.

Challenge yourself with adaptive solo ACT practice sessions on Grockit.

1. The answer must be based on the passage. Even if the question seems really vague, the correct choice will be based on some sort of implication from the passage. ALWAYS go back to the passage to make sure you understand the ideas in the lines the question asks about. You’re like a detective looking for clues. They may be very subtle, but the clues must be there, otherwise the test-maker could never have written the question!

2. It is not a matter of opinion. When you read the answer choices, remember that you are looking for a choice that is the closest to what is directly supported by the passage, not for a choice that sounds plausible to you. Only ONE choice can be correct using the given passage. If you’ve narrowed it down to two choices, check to make sure you aren’t being swayed by one that “seems reasonable” but has no support behind it.

3. You can always make some kind of prediction. Even for open-ended questions, you need to take a few seconds to look back to the passage and think how YOU would answer the question. It’s okay to make prediction like, “Something in terms of…” or “A choice that has something to do with…” It is always better to think critically on your own and give your brain a few extra seconds to process the information than to jump straight to the answer choices.

In the final paragraph of the passage, the author is assuming that

A                  modern writing takes realism too far.

B                  quality writing is a matter of natural ability more than anything else.

C                  there is no easy way to draw the line between a realistic piece of writing and a work that is more fantastic.

D                  the only true reflection of artistic merit is the degree to which the writer is able to stylistically conform to the needs and desires of his society.

E                  the typical reader, when evaluating a work of fiction, will judge it by how clearly it fulfills a narrative purpose.

Let’s go back to that final paragraph:

What escapes the minds of the masses is that, taken
past a certain point, realism is not art. Neither
unsatisfying conclusions, nor irritating characters, nor
obscure motives are indications of the literary talents
(45)       of the author. The older, mythic characters may be drawn
with a broad brush, and may possess a simplicity and
singularity of purpose that finds no parallel in
day-to-day life, but that simplicity is not a sign of an
author lacking in subtlety. Rather, a purposeful author
(50)       will have purposeful characters. Whether the story is
meant to illustrate moral principles, explore character
types, or simply entertain, a quality work of art must
have a purpose.

The question wants us to make a logical conclusion, what is the author assuming is true? We can summarize, or bullet-point, his main ideas and opinions, sentence by sentence.

-        Masses don’t get that realism isn’t art.

-        3 characteristics the author doesn’t like (likely has to do with realism)

-        Older, simpler characters is  what the author likes, even though simple + not like everyday life

-        Wants purposeful characters & art to have a purpose

The correct answer will reflect one of these 4 ideas. When we go back to the choices to evaluate, it’s clear that the correct answer is A. It is best supported by the author’s claim that the masses in today’s world don’t get that realism isn’t art. That implies that realism is popular, and that the masses think it IS art. Notice also the use of the phrase “day-to-day life” implying a timeline.

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Note that if the change in the equation is that x is multiplied or divided, then the slope of the equation will be affected, and the shape of the linear equation will change. Remember that for the x-coordinate, even when we are adding to the x-coordinate, the graph will shift to the left (in the negative direction on the x-axis). It’s almost the opposite of what you’d expect! If you are ever in any doubt about the rules of translation, you can always pick values for x and plug them into the new function!

Let’s check out a couple of these Qualitative Behavior questions from the Grockit question bank!

1. The function h is defined by h(x) = ax² + bx + c, where a is a negative constant and c is a positive constant. Which of the following graphs could represent h?

The equation ax² + bx + c describes a parabola, and the constant c represents how far above or below the x-axis the vertex of the parabola lies. We know that c in this case is positive, so the correct graph should show a parabola with a vertex that lies above the x-axis. The correct answer would look like the parabola pictured here.

Let’s look at another question which tests a similar concept:

2. In the xy-coordinate system, the graphs of y=x³-5 and y=-x+c² intersect at point (3,r). What is a possible value of c?

Plug the given value of x into the first equation to find the value of y.
y=x³-5
y=3³-5
y=27-5
y=22
Since the graphs intersect at the same point, these values for x and y would also be accurate for the second equation. y=-x+c²
22=-3+c²
25=c²
c = 5 or -5; only 5 is an available option.

3. The figure provided shows the graph of a quadratic function f whose minimum value is f(1).
If f(a) = 0, which of the following could be the value of a?

A                  0

B                  1

C                  2

D                  3

E                  5

Quadratic equations form symmetrical graphs. If f (1) is the minimum point of the graph, then moving 1 unit right on the x axis will yield the same vertical change on the function from that minimum as moving 1 unit left does. The goal is find the value of a, such that f(a) = 0. This is the x-value at which the graph passes through the x-axis. We are told that f(1) is the lowest point of the graph. Clearly, according to the figure, the lowest point is not equal to zero. So f(1) ≠ 0.

Notice that the y-intercept of the graph is negative. Just looking at the graph makes it clear that x does not equal 0 when y = 0. If the graph does not pass through the x-axis at x = 0, then it must not pass through the x-axis at x = 2, since both are exactly 1 unit from the turning point of the graph.

It’s down to choices D and E. If the graph were to pass through the x-axis as x = 3, then it must also pass through the x-axis at x = -1, since both -1 and 3 are 2 units from the turning point at x = 1. We can see that the graph does not pass through the x-axis at x = -1. The only possible point at which f (a) = 0 is when a = 5.

Ready to try some more Qualitative Behavior questions? Choose to work by yourself in Grockit’s Solo Practice or join a Group Game in the Grockit SAT lobby to study with others!