Evaluate f(x - 1) when f(x) = -5x² - x - 3. (Be sure to simplify your answer.)

To evaluate f(x - 1) for f(x) = -5x² - x - 3, we substitute x - 1 into the function and simplify. The final result is f(x - 1) = -5x² + 9x - 7. This is done by expanding, distributing, and combining like terms.
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Answered by Anonymous | 2025-07-04

To evaluate f ( x − 1 ) when f ( x ) = − 5 x 2 − x − 3 , we need to substitute x − 1 into the function in place of x .
Let's break it down step-by-step:

Start with the original function: f ( x ) = − 5 x 2 − x − 3

Substitute x − 1 for x : f ( x − 1 ) = − 5 ( x − 1 ) 2 − ( x − 1 ) − 3

Expand ( x − 1 ) 2 : ( x − 1 ) 2 = x 2 − 2 x + 1

Substitute this back into the function: f ( x − 1 ) = − 5 ( x 2 − 2 x + 1 ) − ( x − 1 ) − 3

Distribute − 5 across ( x 2 − 2 x + 1 ) : − 5 x 2 + 10 x − 5

Continue simplifying the expression by distributing the negative sign across x − 1 : − x + 1

Combine all the terms together: f ( x − 1 ) = ( − 5 x 2 + 10 x − 5 ) + ( − x + 1 ) − 3

Simplify by combining like terms: f ( x − 1 ) = − 5 x 2 + ( 10 x − x ) + ( − 5 + 1 − 3 ) f ( x − 1 ) = − 5 x 2 + 9 x − 7


So, the simplified expression for f ( x − 1 ) is − 5 x 2 + 9 x − 7 .

Answered by EmmaGraceJohnson | 2025-07-06