Perfect1600

Digital SAT · Solve it in Desmos

How to Solve Graph Features on Desmos (Digital SAT)

Because Desmos labels each feature exactly, clicking is the surest route on nearly all of these. Read from the equation only when a form hands the feature over at a glance, like the y-intercept from the constant.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for graph features

The Desmos steps

  1. 1

    Graph the function

    Type it as y = ... in Desmos to see the curve.

  2. 2

    Click the feature

    The x-axis crossing for a zero, the y-axis crossing for the y-intercept, the turning point for the vertex; each gets labeled coordinates.

  3. 3

    Take the value asked

    Read the x, the y, or the full point from the labeled dot.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example
f(x)=(x−2)2f(x) = (x - 2)^2 Which of the following tables gives three values of x and their corresponding values of f(x)f(x) for the function f?
A
xf(x)
14
23
34
xf(x)
11
20
31
C
xf(x)
11
20
35
D
xf(x)
10
21
34

A: At x=1x = 1, the function f gives f(1)=1f(1) = 1, not 4 as shown, so this table does not represent it.

B: Every value in this table satisfies the function f, so it correctly represents the relationship.

C: At x=3x = 3, the function f gives f(3)=1f(3) = 1, not 5 as shown, so this table does not represent it.

D: At x=1x = 1, the function f gives f(1)=1f(1) = 1, not 0 as shown, so this table does not represent it.

Explanation

Substitute each x-value into the function f and compare the result with the value in the table. The correct table is the one whose every value matches; a table with even one value that does not satisfy the function f is incorrect.

Medium example
Consider the function ff given by f(x)=x2−64f(x)=x^2-64. What is the positive xx-intercept of the graph of ff?
A
−8-8
B
00
88
D
6464

A: Incorrect. −8-8 is the negative xx-intercept.

B: Incorrect. f(0)=−64≠0f(0)=-64\ne0.

C: Correct. x2−64=0x^2-64=0 gives x=±8x=\pm8; the positive one is 8.

D: Incorrect. 64 is the constant, not an xx-intercept.

Explanation

x^2 = 64 gives x = +-8; positive is 8.

Hard example
Consider the function ff given by f(x)=−2(x+3)2+8f(x)=-2(x+3)^2+8. What is the maximum value of ff?
A
−3-3
B
−2-2
C
33
88

A: Incorrect. −3-3 is the xx-coordinate of the vertex, not the value.

B: Incorrect. −2-2 is the leading coefficient, not the value.

C: Incorrect. 3 is part of the vertex xx-coordinate, not the maximum.

D: Correct. In −2(x+3)2+8-2(x+3)^2+8, the parabola opens down, so the maximum value is 8.

Explanation

Vertex form: max value 8 (at x = -3).

Try it with the calculator

Question 1easy

f(x)=x2−3f(x) = x^2 - 3 Which of the following tables gives three values of x and their corresponding values of f(x)f(x) for the function f?

Question 2easy

In the xyxy-plane, the graph of f(x)=(x−2)(x+6)f(x) = (x - 2)(x + 6) is a parabola. What is the xx-coordinate of the vertex of this parabola?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve graph features questions on the SAT?

Because Desmos labels each feature exactly, clicking is the surest route on nearly all of these. Read from the equation only when a form hands the feature over at a glance, like the y-intercept from the constant.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master graph features, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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