Re-write the quadratic function below in Standard Form y=-6(x+2)(x-7) Answer: y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as the FOIL method for binomials). y = -6(x + 2)(x - 7) First, distribute the -6 to the binomials (x + 2) and (x - 7). y = -6[(x)(x) + (x)(-7) + (2)(x) + (2)(-7)]Simplify Expression: Simplify the expression by multiplying the terms inside the brackets. y = -6[x^2 - 7x + 2x - 14] Combine like terms inside the brackets. y = -6[x^2 - 5x - 14]Distribute -6: Distribute the -6 across each term inside the brackets. y = -6(x^2) + 6(5x) + 6(14) y = -6x^2 + 30x + 84Write in Standard Form: Write the final expression in Standard Form, which is y = ax^2 + bx + c. y = -6x^2 + 30x + 84 This is the quadratic function in Standard Form.

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Multiply two binomials

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

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y=-6(x+2)(x-7)

\newline

Answer:

y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as the FOIL method for binomials). $\newline$ $y = -6(x + 2)(x - 7)$ $\newline$ First, distribute the $-6$ to the binomials $(x + 2)$ and $(x - 7)$ . $\newline$ $y = -6[(x)(x) + (x)(-7) + (2)(x) + (2)(-7)]$
Simplify Expression: Simplify the expression by multiplying the terms inside the brackets. $\newline$ $y = -6[x^2 - 7x + 2x - 14]$ $\newline$ Combine like terms inside the brackets. $\newline$ $y = -6[x^2 - 5x - 14]$
Distribute $-6$ : Distribute the $-6$ across each term inside the brackets. $\newline$ $y = -6(x^2) + 6(5x) + 6(14)$ $\newline$ $y = -6x^2 + 30x + 84$
Write in Standard Form: Write the final expression in Standard Form, which is $y = ax^2 + bx + c$ . $\newline$ $y = -6x^2 + 30x + 84$ $\newline$ This is the quadratic function in Standard Form.