How to Evaluate a Quadratic Function

Precalculus · Functions and domains

How to Evaluate a Quadratic Function

Problem

f(x) = 2x^2 - 3x + 1,\quad x = 2

Answer

f(2) = 3

A function is a rule that pairs each input with one output. To evaluate it, substitute the input and simplify using the order of operations.

Step-by-step solution

Substitute 2 for every x.
$f(2) = 2(2)^2 - 3(2) + 1$
Why: Evaluating a function means replacing the input everywhere it appears.
Apply the exponent.
$2(4) - 3(2) + 1$
Why: Exponents come before multiplication in the order of operations.
Multiply.
$8 - 6 + 1$
Why: Each term is now a single number.
Add and subtract from left to right.
$8 - 6 + 1 = 3$
Why: Left-to-right order gives the same result as combining carefully.

Common mistakes

Squaring 2x and getting 4x squared. Only x is squared.
Writing -3(2) as +6. The coefficient keeps its negative sign.
Doing 8 - (6 + 1) instead of 8 - 6 + 1. Addition and subtraction go left to right.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

$f(1)$

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$0$
$f(0)$

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$1$
$f(-1)$

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$6$
$f(3)$

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$10$
$f(-2)$

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$15$