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].
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].
