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

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Evaluating a Mathematical Function

Example

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

To evaluate the quadratic function $f(x) = 3x^2 - 2x + 1$ 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 $f(3) = 3(3)^2 - 2(3) + 1$ . Simplify the exponent to get $3(9) - 2(3) + 1$ . Multiply to obtain $27 - 6 + 1$ . Combine the terms to find $f(3) = 22$ . - Evaluate $f(-1)$ : Replace $x$ with $-1$ using parentheses to preserve the negative signs: $f(-1) = 3(-1)^2 - 2(-1) + 1$ . Simplifying the exponent gives $3(1) - (-2) + 1$ . Multiply to obtain $3 + 2 + 1$ . Simplify to find $f(-1) = 6$ . - Evaluate $f(t)$ : Replace $x$ with the variable $t$ : $f(t) = 3(t)^2 - 2(t) + 1$ . Simplify to yield $f(t) = 3t^2 - 2t + 1$ . This illustrates that evaluating a function with a variable produces an algebraic expression rather than a numerical value.

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Updated 2026-05-06

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OpenStax Intermediate Algebra

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