Re-write the quadratic function below in Standard Form y=-2(x+9)(x-4) Answer: y=

Distribute -2 to product: We distribute -2 to the product of (x + 9) and (x - 4). y = -2[(x + 9)(x - 4)] y = -2[x(x - 4) + 9(x - 4)] Now we will distribute x to (x - 4) and 9 to (x - 4).Distribute x and 9: Distribute x to (x - 4). x(x - 4) = x^2 - 4x Now distribute 9 to (x - 4). 9(x - 4) = 9x - 36 Combine the two results.Combine distributed terms: Combine the distributed terms. y = -2(x^2 - 4x + 9x - 36) Now we will combine like terms within the parentheses.Combine like terms: Combine like terms. y = -2(x^2 + 5x - 36) Now we distribute -2 to each term inside the parentheses.Distribute -2 to each term: Distribute -2 to each term. y = -2(x^2) - 2(5x) - 2(-36) y = -2x^2 - 10x + 72 This is the quadratic function in Standard Form.

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Algebra 1

Multiply two binomials

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Q. Re-write the quadratic function below in Standard Form

\newline

y=-2(x+9)(x-4)

\newline

Answer:

y=

Distribute $-2$ to product: We distribute $-2$ to the product of $(x + 9)$ and $(x - 4)$ .
$y = -2[(x + 9)(x - 4)]$
$y = -2[x(x - 4) + 9(x - 4)]$
Now we will distribute $x$ to $(x - 4)$ and $9$ to $(x - 4)$ .
Distribute $x$ and $9$ : Distribute $x$ to $(x - 4)$ .
$x(x - 4) = x^2 - 4x$
Now distribute $9$ to $(x - 4)$ .
$9(x - 4) = 9x - 36$
Combine the two results.
Combine distributed terms: Combine the distributed terms. $\newline$ $y = -2(x^2 - 4x + 9x - 36)$ $\newline$ Now we will combine like terms within the parentheses.
Combine like terms: Combine like terms. $\newline$ $y = -2(x^2 + 5x - 36)$ $\newline$ Now we distribute $-2$ to each term inside the parentheses.
Distribute $-2$ to each term: Distribute $-2$ to each term. $\newline$ $y = -2(x^2) - 2(5x) - 2(-36)$ $\newline$ $y = -2x^2 - 10x + 72$ $\newline$ This is the quadratic function in Standard Form.