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Evaluating a Mathematical Function

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Example: Evaluating the Function $f(x) = 2x^2 + 4x - 3$

To evaluate the quadratic function $f(x) = 2x^2 + 4x - 3$ for a specific value or variable, substitute that value for $x$ in the expression and simplify using the order of operations: - Evaluate $f(2)$ : Replace $x$ with $2$ to get $f(2) = 2(2)^2 + 4(2) - 3$ . Simplify the exponent to get $2(4) + 4(2) - 3$ . Multiply to obtain $8 + 8 - 3$ . Combine the terms to find $f(2) = 13$ . - Evaluate $f(-3)$ : Replace $x$ with $-3$ using parentheses to preserve the negative signs: $f(-3) = 2(-3)^2 + 4(-3) - 3$ . Simplifying the exponent gives $2(9) - 12 - 3$ . Multiply to obtain $18 - 12 - 3$ . Simplify to find $f(-3) = 3$ . - Evaluate $f(h)$ : Replace $x$ with the variable $h$ : $f(h) = 2(h)^2 + 4(h) - 3$ . Simplify to yield $f(h) = 2h^2 + 4h - 3$ . The same substitution procedure applies when evaluating a function with a variable instead of a constant.

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Updated 2026-05-06

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OpenStax Intermediate Algebra

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