Given the function f(x)=-(1)/(4)x^(2)+4, find the value of f(-1) in simplest form. Answer:

Substitute x with -1: Substitute x with -1 in the function f(x) = -(1/4)x^2 + 4. Reasoning: To find f(-1), we need to replace x with -1 in the function and simplify. Calculation: f(-1) = -(1/4)(-1)^2 + 4 = -(1/4)(1) + 4 = -1/4 + 4Convert 4 to fraction: Convert 4 to a fraction with a denominator of 4 to combine with -1/4. Reasoning: To add or subtract fractions, they must have a common denominator. Calculation: 4 = 16/4, so -1/4 + 4 becomes -1/4 + 16/4Add the fractions: Add the fractions -1/4 and 16/4. Reasoning: Now that we have a common denominator, we can add the numerators. Calculation: -1/4 + 16/4 = (16 - 1)/4 = 15/4

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Given the function
f(x)=-(1)/(4)x^(2)+4, find the value of
f(-1) in simplest form.
Answer:

Given the function $f(x)=-\frac{1}{4} x^{2}+4$ , find the value of $f(-1)$ in simplest form. $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. Given the function

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

, find the value of

f(-1)

in simplest form.

\newline

Answer:

Substitute $x$ with $-1$ : Substitute $x$ with $-1$ in the function $f(x) = -(\frac{1}{4})x^2 + 4$ . Reasoning: To find $f(-1)$ , we need to replace $x$ with $-1$ in the function and simplify. Calculation: $f(-1) = -(\frac{1}{4})(-1)^2 + 4 = -(\frac{1}{4})(1) + 4 = -\frac{1}{4} + 4$
Convert $4$ to fraction: Convert $4$ to a fractions" target="_blank" class="backlink">fraction with a denominator of $4$ to combine with $-\frac{1}{4}$ . $\newline$ Reasoning: To add or subtract fractions, they must have a common denominator. $\newline$ Calculation: $4 = \frac{16}{4}$ , so $-\frac{1}{4} + 4$ becomes $-\frac{1}{4} + \frac{16}{4}$
Add the fractions: Add the fractions $-\frac{1}{4}$ and $\frac{16}{4}$ . $\newline$ Reasoning: Now that we have a common denominator, we can add the numerators. $\newline$ Calculation: $-\frac{1}{4} + \frac{16}{4} = \frac{16 - 1}{4} = \frac{15}{4}$