SAT Math formula sheet · all 24 · Advanced Math · #8 of 24

Quadratic equations on the SAT: How It Is Tested

Nonlinear functions

Quadratics diagram for the SAT: Know the 3 quadratic forms and what information each one gives you. Know the common questions and what they represent in
What it is really testingKnow the 3 quadratic forms and what information each one gives you. Know the common questions and what they represent in context. Understand symmetry through the vertex of a quadratic.

The question from the sheet

Hard
SAT Advanced Mathanswer -12
Function ff is a quadratic function where f(−18)=0f(-18) = 0 and f(−6)=0f(-6) = 0. The graph of y=f(x)y = f(x) in the xyxy-plane has a vertex at (r,−36)(r, -36). What is the value of rr?
Student-produced response: -12

How the diagram applies

  1. f(−18)=0f(-18) = 0 and f(−6)=0f(-6) = 0 are the x-intercepts, so factored form is f(x)=a(x+18)(x+6)f(x) = a(x + 18)(x + 6).
  2. A parabola is symmetric: the vertex sits exactly halfway between the x-intercepts.
  3. r=−18+(−6)2=−12r = \dfrac{-18 + (-6)}{2} = -12.

Answer: -12

That is 1 of 24.

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Common Questions

It comes up as an SAT nonlinear functions question. Know the 3 quadratic forms and what information each one gives you. Know the common questions and what they represent in context. Understand symmetry through the vertex of a quadratic.

f(-18) = 0 and f(-6) = 0 are the x-intercepts, so factored form is f(x) = a(x + 18)(x + 6). A parabola is symmetric: the vertex sits exactly halfway between the x-intercepts. r = -18 + (-6)2 = -12.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Quadratics 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.