1Cademy - Example: Evaluating the Function $$f(x) = 2x^2 + 3x

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Evaluating a Mathematical Function

Example

Example: Evaluating the Function $f(x) = 2x^2 + 3x - 1$

To evaluate the quadratic function $f(x) = 2x^2 + 3x - 1$ for a specific value or variable, substitute that value for $x$ in the expression and simplify using the order of operations:

Evaluate $f(3)$ : Replace $x$ with $3$ to get $f(3) = 2(3)^2 + 3(3) - 1$ . Simplify the exponent to get $2(9) + 3(3) - 1$ . Multiply to obtain $18 + 9 - 1$ . Combine the terms to find $f(3) = 26$ .
Evaluate $f(-2)$ : Replace $x$ with $-2$ using parentheses to preserve the negative signs: $f(-2) = 2(-2)^2 + 3(-2) - 1$ . Simplifying the exponent gives $2(4) - 6 - 1$ . Multiply to obtain $8 - 6 - 1$ . Simplify to find $f(-2) = 1$ .
Evaluate $f(a)$ : Replace $x$ with the variable $a$ : $f(a) = 2(a)^2 + 3(a) - 1$ . Simplify to yield $f(a) = 2a^2 + 3a - 1$ . The same substitution procedure applies when evaluating a function with a variable rather than a constant.

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Updated 2026-05-06

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OpenStax Intermediate Algebra

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