High School

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Select the correct answer.

Which of these is the standard form of the following function?

[tex] f(x) = -9(x+5)^2 + 4 [/tex]

A. [tex] f(x) = -9x^2 - 180x - 221 [/tex]

B. [tex] f(x) = 9x^2 - 180x + 221 [/tex]

C. [tex] f(x) = 9x^2 - 90x - 221 [/tex]

D. [tex] f(x) = -9x^2 - 90x - 221 [/tex]

Answer :

Let's find the standard form of the function [tex]\( f(x) = -9(x + 5)^2 + 4 \)[/tex].

To convert this to standard form, we need to expand the expression [tex]\(-9(x + 5)^2\)[/tex], and then add 4.

1. Expand [tex]\((x + 5)^2\)[/tex]:

[tex]\[
(x + 5)^2 = x^2 + 10x + 25
\][/tex]

2. Multiply the expression by -9:

[tex]\[
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225
\][/tex]

3. Add 4 to the expanded expression:

[tex]\[
f(x) = -9x^2 - 90x - 225 + 4
\][/tex]

4. Combine like terms:

[tex]\[
f(x) = -9x^2 - 90x - 221
\][/tex]

Therefore, the standard form of the function is [tex]\( f(x) = -9x^2 - 90x - 221 \)[/tex].

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