Answer :
To find the standard form of the function [tex]\( f(x) = -9(x+5)^2 + 4 \)[/tex], let's go through the steps of expanding and simplifying it.
1. Expand the Square: Start by expanding the square term [tex]\((x+5)^2\)[/tex].
[tex]\((x+5)^2 = x^2 + 10x + 25\)[/tex].
2. Multiply by -9: Next, multiply each term inside the parenthesis 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 4 from the original equation.
[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 from the given options is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]
1. Expand the Square: Start by expanding the square term [tex]\((x+5)^2\)[/tex].
[tex]\((x+5)^2 = x^2 + 10x + 25\)[/tex].
2. Multiply by -9: Next, multiply each term inside the parenthesis 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 4 from the original equation.
[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 from the given options is:
[tex]\[ f(x) = -9x^2 - 90x - 221 \][/tex]
