Sure, let's rewrite the quadratic function [tex]\( y = -9(x - 4)(x + 1) \)[/tex] in Standard Form.
1. Start with the given quadratic function:
[tex]\[
y = -9(x - 4)(x + 1)
\][/tex]
2. First, expand the expression [tex]\((x - 4)(x + 1)\)[/tex] using the distributive property:
[tex]\[
(x - 4)(x + 1) = x \cdot x + x \cdot 1 - 4 \cdot x - 4 \cdot 1
\][/tex]
Simplifying this, we have:
[tex]\[
(x - 4)(x + 1) = x^2 + x - 4x - 4
\][/tex]
Combining like terms, we get:
[tex]\[
x^2 + x - 4x - 4 = x^2 - 3x - 4
\][/tex]
3. Now multiply the expanded quadratic expression by -9:
[tex]\[
y = -9(x^2 - 3x - 4)
\][/tex]
Distribute -9 to each term inside the parentheses:
[tex]\[
y = -9x^2 + 27x + 36
\][/tex]
So, the quadratic function [tex]\( y = -9(x - 4)(x + 1) \)[/tex] rewritten in Standard Form is:
[tex]\[
y = -9x^2 + 27x + 36
\][/tex]
