SAT Math Domain

SAT Advanced Math: Quadratics & Polynomials

Advanced Math tests your ability to manipulate complex algebraic expressions, solve quadratic and higher-degree polynomial equations, and analyze exponential and radical functions.

Practice Nonlinear Functions, Quadratics & Polynomials Questions Estimate Math Score

What the SAT Tests in Nonlinear Functions, Quadratics & Polynomials

Quadratic equations: factoring, vertex form, quadratic formula, and the discriminant

Polynomial arithmetic, polynomial division, and root-factor theorems

Exponential growth and decay models

Radical and rational equations and identifying extraneous solutions

Formulas & Shortcuts

High-Yield Formulas & Desmos Rules

Quadratic Formulax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Finds real and complex roots of ax^2 + bx + c = 0.

Vertex Coordinatesh = -\frac{b}{2a}, \quad k = f(h)

Gives the coordinates of the parabola maximum or minimum.

Discriminant Rules\Delta = b^2 - 4ac

>0: 2 real roots; =0: 1 real root; <0: 0 real roots (2 complex).

Exponential Modelf(t) = a(1 + r)^t

a is initial value, r is percentage growth rate per period t.

Common Student Traps

•Forgetting to check for extraneous solutions in rational and radical equations.
•Misidentifying the vertex form y = a(x - h)^2 + k (remembering (x - h) means the x-coordinate is positive h).
•Confusing linear change with exponential percent growth.

Proven Study Strategies

•Use Desmos sliders to quickly find unknown constants like k in quadratic vertex problems.
•Memorize the vertex x-coordinate formula h = -b / (2a) to save valuable calculation time.
•Always substitute roots back into square-root equations to discard fake extraneous roots.

Example Questions & Solutions

Step-by-step walkthroughs

Example Question #1hard Difficulty

For the quadratic function f(x) = 2x^2 - 12x + k, the vertex of the graph is at (h, -5). What is the value of constant k?

A.13

B.18

C.-5

D.23

Solution (Option A):

h = -b / (2a) = -(-12) / (2 * 2) = 12 / 4 = 3. Substituting x = 3 and f(3) = -5: -5 = 2(3)^2 - 12(3) + k => -5 = 18 - 36 + k => -5 = -18 + k => k = 13.

Practice Questions in this Skill

hard Difficulty

SAT Quadratic Vertex Practice Question

For the quadratic function f(x) = 2x^2 - 12x + k, the graph has a vertex at (h, -5). What is the value of constant k?

Frequently Asked Questions

How many Advanced Math questions are on the Digital SAT?

Advanced Math makes up about 13 to 15 questions (roughly 35% of the total Math section).