SAT Math · Advanced Math

Nonlinear Functions on the Digital SATWhat it tests, how to approach it, and where students get trapped

Quadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.

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Nonlinear Functions in Our Question Bank

122

Total questions

Easy

Medium

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Advanced Math.

What the SAT Actually Tests

The largest Advanced Math category: quadratic functions (vertex, zeros, axis of symmetry), exponential growth and decay, and polynomial behavior. Questions ask you to interpret vertex form a(x−h)² + k, identify growth factors in f(t) = a·b^t, and connect equations to the shape and key points of their graphs.

Learn what each form reveals instantly: factored form gives zeros, vertex form gives the max/min point, standard form gives the y-intercept. For exponentials, the base b is the growth factor — b = 1.04 means 4% growth per period, b = 0.72 means 28% decay. When a question mixes forms, convert to whichever exposes the feature being asked about.

Original Nonlinear Functions Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy

The function p is defined by p(x) = 4x² − 14. For what positive value of x is p(x) = 50?

A)2B)3C)4D)16

Question 2medium

The function h(t) = a - 16t² estimates an object's height, in feet, above the ground t seconds after the object is dropped, where a is a constant. The function estimates that the object is 256 feet above the ground when it is dropped at t = 0. Approximately how many seconds after being dropped does the function estimate the object will hit the ground?

A)2B)16C)4D)8

Traps to Avoid

Reading the vertex of y = (x − 3)² + 5 as (−3, 5) — the sign inside the parentheses flips.
Confusing the decay rate with the decay factor: 28% decay means multiplying by 0.72, not by 0.28.
Assuming a function's maximum is its y-intercept because both are 'the number at the end' of different forms.

Want more official questions for this skill?

The College Board Student Question Bank can filter official SAT questions by section, domain, skill, and difficulty. Read our question-bank workflow guide before choosing a set.

More Advanced Math Skills

Equivalent Expressions

Rewriting algebraic expressions — factoring, expanding, combining rational expressions, and applying exponent rules to show two forms are equivalent.

Nonlinear Equations & Systems

Solving quadratic, radical, rational, and exponential equations, plus systems that mix a line with a curve — including discriminant reasoning.

Function Notation

Evaluating and composing functions written as f(x), interpreting what f(a) = b means, and translating between notation, tables, and graphs.

Continue With Advanced Math Practice

Practice is sorted by domain and difficulty. On the Free plan you get the first 5 questions of each difficulty in Advanced Math. Pro opens every question in the bank.

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Last reviewed August 29, 2026 · Grind1600 Editorial Team