Answer :
Let's find the standard form of the function [tex]\( f(x) = -9(x+5)^2 + 4 \)[/tex].
1. Expand the Squared Term:
[tex]\((x + 5)^2\)[/tex] can be expanded using the formula [tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex].
[tex]\[
(x + 5)^2 = x^2 + 10x + 25
\][/tex]
2. Distribute the Coefficient:
Now, multiply each term in the expression by [tex]\(-9\)[/tex]:
[tex]\[
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225
\][/tex]
3. Add the Constant Term:
Finally, add the constant term [tex]\(4\)[/tex] to the expression:
[tex]\[
-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221
\][/tex]
So, the standard form of the function is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]
The correct answer is the third option:
[tex]\( f(x) = -9x^2 - 90x - 221 \)[/tex]
1. Expand the Squared Term:
[tex]\((x + 5)^2\)[/tex] can be expanded using the formula [tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex].
[tex]\[
(x + 5)^2 = x^2 + 10x + 25
\][/tex]
2. Distribute the Coefficient:
Now, multiply each term in the expression by [tex]\(-9\)[/tex]:
[tex]\[
-9(x^2 + 10x + 25) = -9x^2 - 90x - 225
\][/tex]
3. Add the Constant Term:
Finally, add the constant term [tex]\(4\)[/tex] to the expression:
[tex]\[
-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221
\][/tex]
So, the standard form of the function is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]
The correct answer is the third option:
[tex]\( f(x) = -9x^2 - 90x - 221 \)[/tex]
