Given the function f(x)=-2x-(1)/(4)x^(2), then what is f(x-2) as a simplified polynomial? Answer:

Substitute and Distribute: To find f(x-2), we need to substitute (x-2) for every instance of x in the function f(x) = -2x - (1/4)x^2. f(x-2) = -2(x-2) - (1/4)(x-2)^2Expand (x-2)^2: First, distribute the -2 across the (x-2) term. f(x-2) = -2x + 4 - (1/4)(x-2)^2Substitute Expanded Term: Next, expand the (x-2)^2 term. (x-2)^2 = x^2 - 4x + 4Distribute -1/4: Now, substitute the expanded (x-2)^2 back into the equation. f(x-2) = -2x + 4 - (1/4)(x^2 - 4x + 4)Combine Like Terms: Distribute the -1/4 across the x^2 - 4x + 4. f(x-2) = -2x + 4 - (1/4)x^2 + x - 1Reorder to Standard Form: Combine like terms. f(x-2) = -2x + x + 4 - 1 - (1/4)x^2 f(x-2) = -x + 3 - (1/4)x^2Reorder the terms to write the polynomial in standard form, which is from highest degree to lowest degree. f(x-2) = -(1/4)x^2 - x + 3

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Given the function
f(x)=-2x-(1)/(4)x^(2), then what is
f(x-2) as a simplified polynomial?
Answer:

Given the function $f(x)=-2 x-\frac{1}{4} x^{2}$ , then what is $f(x-2)$ as a simplified polynomial? $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find an equation

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Q. Given the function

f(x)=-2 x-\frac{1}{4} x^{2}

, then what is

f(x-2)

as a simplified polynomial?

\newline

Answer:

Substitute and Distribute: To find $f(x-2)$ , we need to substitute $(x-2)$ for every instance of $x$ in the function $f(x) = -2x - \frac{1}{4}x^2$ .
$f(x-2) = -2(x-2) - \frac{1}{4}(x-2)^2$
Expand $(x-2)^2$ : First, distribute the $-2$ across the $(x-2)$ term. $\newline$ $f(x-2) = -2x + 4 - (\frac{1}{4})(x-2)^2$
Substitute Expanded Term: Next, expand the $(x-2)^2$ term. $\newline$ $(x-2)^2 = x^2 - 4x + 4$
Distribute $-\frac{1}{4}$ : Now, substitute the expanded $(x-2)^2$ back into the equation. $\newline$ $f(x-2) = -2x + 4 - \left(\frac{1}{4}\right)(x^2 - 4x + 4)$
Combine Like Terms: Distribute the $-\frac{1}{4}$ across the $x^2 - 4x + 4$ . $\newline$ $f(x-2) = -2x + 4 - \left(\frac{1}{4}\right)x^2 + x - 1$
Reorder to Standard Form: Combine like terms. $\newline$ $f(x-2) = -2x + x + 4 - 1 - \frac{1}{4}x^2$ $\newline$ $f(x-2) = -x + 3 - \frac{1}{4}x^2$
Reorder to Standard Form: Combine like terms. $\newline$ $f(x-2) = -2x + x + 4 - 1 - \frac{1}{4}x^2$ $\newline$ $f(x-2) = -x + 3 - \frac{1}{4}x^2$ Reorder the terms to write the polynomial in standard form, which is from highest degree to lowest degree. $\newline$ $f(x-2) = -\frac{1}{4}x^2 - x + 3$