1Cademy - Evaluating the Polynomial Function $$g(x) = 5x^2 - x

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Evaluating a Mathematical Function

Example

Evaluating the Polynomial Function $g(x) = 5x^2 - x - 4$

To evaluate the polynomial function $g(x) = 5x^2 - x - 4$ for specific values, substitute the value for the variable $x$ and simplify using the order of operations:

Evaluate $g(-2)$ : Substitute $-2$ for $x$ to obtain $g(-2) = 5(-2)^2 - (-2) - 4$ . Simplifying the exponent gives $5(4) + 2 - 4$ . Multiply to get $20 + 2 - 4$ , and simplify to find $g(-2) = 18$ .
Evaluate $g(-1)$ : Substitute $-1$ for $x$ to obtain $g(-1) = 5(-1)^2 - (-1) - 4$ . Simplifying the exponent gives $5(1) + 1 - 4$ . Multiply to get $5 + 1 - 4$ , and simplify to find $g(-1) = 2$ .
Evaluate $g(0)$ : Substitute $0$ for $x$ to obtain $g(0) = 5(0)^2 - 0 - 4$ . Simplifying the exponent gives $5(0) - 0 - 4$ , which simplifies to $g(0) = -4$ .

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Updated 2026-04-29

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OpenStax Intermediate Algebra

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