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

Understand function transformation: Understand the function transformation. We need to find f(x+2), which means we will substitute x+2 into the function f(x) in place of x.Substitute x+2 into function: Substitute x+2 into the function. f(x) = -x^2 + 1/4, so f(x+2) = -(x+2)^2 + 1/4Expand square term: Expand the square term. f(x+2) = -[(x+2)(x+2)] + 1/4 f(x+2) = -(x^2 + 4x + 4) + 1/4Distribute and simplify: Distribute the negative sign and simplify. f(x+2) = -x^2 - 4x - 4 + 1/4Combine like terms: Combine like terms. Since there are no like terms with -4 and 1/4, we convert -4 to a fraction with a denominator of 4 to combine them. -4 = -16/4 f(x+2) = -x^2 - 4x - 16/4 + 1/4 f(x+2) = -x^2 - 4x - 15/4

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

Given the function $f(x)=-x^{2}+\frac{1}{4}$ , 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

Full solution

Q. Given the function

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

, then what is

f(x+2)

as a simplified polynomial?

\newline

Answer:

Understand function transformation: Understand the function transformation. $\newline$ We need to find $f(x+2)$ , which means we will substitute $x+2$ into the function $f(x)$ in place of $x$ .
Substitute $x+2$ into function: Substitute $x+2$ into the function. $f(x) = -x^2 + \frac{1}{4}$ , so $f(x+2) = -(x+2)^2 + \frac{1}{4}$
Expand square term: Expand the square term. $\newline$ $f(x+2) = -[(x+2)(x+2)] + \frac{1}{4}$ $\newline$ $f(x+2) = -(x^2 + 4x + 4) + \frac{1}{4}$
Distribute and simplify: Distribute the negative sign and simplify. $f(x+2) = -x^2 - 4x - 4 + \frac{1}{4}$
Combine like terms: Combine like terms. $\newline$ Since there are no like terms with $-4$ and $\frac{1}{4}$ , we convert $-4$ to a fraction with a denominator of $4$ to combine them. $\newline$ $-4 = -\frac{16}{4}$ $\newline$ $f(x+2) = -x^2 - 4x - \frac{16}{4} + \frac{1}{4}$ $\newline$ $f(x+2) = -x^2 - 4x - \frac{15}{4}$