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

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Evaluating a Mathematical Function

Example

Evaluating the Polynomial Function $f(x) = 3x^2 + 2x - 15$

To evaluate the polynomial function $f(x) = 3x^2 + 2x - 15$ for specific values, substitute the value for the variable $x$ and simplify using the order of operations:

Evaluate $f(3)$ : Substitute $3$ for $x$ to obtain $f(3) = 3(3)^2 + 2(3) - 15$ . Simplifying the exponent gives $3(9) + 6 - 15$ . Multiply to get $27 + 6 - 15$ , and simplify to find $f(3) = 18$ .
Evaluate $f(-5)$ : Substitute $-5$ for $x$ to obtain $f(-5) = 3(-5)^2 + 2(-5) - 15$ . Simplifying the exponent gives $3(25) - 10 - 15$ . Multiply to get $75 - 10 - 15$ , and simplify to find $f(-5) = 50$ .
Evaluate $f(0)$ : Substitute $0$ for $x$ to obtain $f(0) = 3(0)^2 + 2(0) - 15$ . Simplifying the exponent gives $3(0) + 0 - 15$ , which simplifies to $f(0) = -15$ .

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Updated 2026-04-29

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OpenStax Intermediate Algebra

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