Quadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.
107
Total questions
54
Easy
27
Medium
26
Hard
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.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. It's given that p(x) = 4x2 - 7. Substituting 3 for x in this equation yields p(3) = 4(3)2 - 7. This is equivalent to p(3) = 4(9) - 7, or p(3) = 36 - 7, which gives p(3) = 29.
Choice A is incorrect. This is the value of p(0) + 12 or may result from subtracting incorrectly.
Choice B is incorrect. This may result from computing 4(3) - 7 + 7 or similar errors without squaring.
Choice D is incorrect. This is the value of 4(3)2 = 36, without subtracting 7.
Correct answer: 3
From f(0) = a · b⁰ = a · 1 = a = 6, so a = 6.
From f(2) = 6 · b² = 54:
b² = 54 / 6
b² = 9
b = 3 (taking the positive value since b > 0 for an exponential function)
The value of b is 3.
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.
107 Nonlinear Functions questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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