SAT Math formula sheet · all 24 · Advanced Math · #9 of 24

Reading a quadratic graph on the SAT: How It Is Tested

Nonlinear functions

Quadratic Interpretations diagram for the SAT: Three points they ask about: the y-intercept is the "starting value," the x-intercept is when it "hits the ground," the
What it is really testingThree points they ask about: the y-intercept is the "starting value," the x-intercept is when it "hits the ground," the vertex is the "max or min." Those are the kinds of words to listen for; they are not always word for word.

The question from the sheet

Hard
SAT Advanced Mathanswer D
The given function f(x)f(x) gives a metal ball's height above the ground f(x)f(x), in inches, xx seconds after it started moving on a track, where 0≤x≤200 \leq x \leq 20. Which of the following is the best interpretation of the vertex of the graph of y=f(x)y = f(x) in the xyxy-plane?
f(x)=116(x−5)2+4f(x) = \frac{1}{16}(x - 5)^{2} + 4
AThe metal ball's height was 5 inches when it started moving
BThe metal ball's minimum height was 5 inches
CThe metal ball's height was 4 inches when it started moving
✓The metal ball's minimum height was 4 inches

How the diagram applies

  1. f(x)=116(x−5)2+4f(x) = \tfrac{1}{16}(x - 5)^{2} + 4 is vertex form, so the vertex is (5,4)(5, 4): know the vertex (h,k)(h, k).
  2. a=116>0a = \tfrac{1}{16} > 0, so the parabola opens up and the vertex is a minimum.
  3. The minimum height was 44 inches, and it happened at x=5x = 5 seconds. The question asks for the height, the yy of the vertex.

Answer: D

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Common Questions

It comes up as an SAT nonlinear functions question. Three points they ask about: the y-intercept is the "starting value," the x-intercept is when it "hits the ground," the vertex is the "max or min." Those are the kinds of words to listen for; they are not always word for word.

f(x) = 116(x - 5)^2 + 4 is vertex form, so the vertex is (5, 4): know the vertex (h, k). a = 116 > 0, so the parabola opens up and the vertex is a minimum. The minimum height was 4 inches, and it happened at x = 5 seconds. The question asks for the height, the y of the vertex.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Quadratic Interpretations is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.