Re-write the quadratic function below in Standard Form y=-7(x+9)(x-1) Answer: y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as FOIL - First, Outer, Inner, Last). We need to multiply each term in the first binomial by each term in the second binomial. y = -7(x + 9)(x - 1) y = -7[(x * x) + (x * -1) + (9 * x) + (9 * -1)]Perform Multiplication: Perform the multiplication for each pair of terms. y = -7[(x^2) - x + 9x - 9]Combine Like Terms: Combine like terms inside the brackets. y = -7[x^2 + (9x - x) - 9] y = -7[x^2 + 8x - 9]Distribute Coefficients: Distribute the -7 across each term inside the brackets. y = -7(x^2) -7(8x) -7(-9) y = -7x^2 - 56x + 63Write in Standard Form: Write the final expression in standard form, which is ax^2 + bx + c. y = -7x^2 - 56x + 63 This is the standard form of the quadratic function.

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

\newline

y=-7(x+9)(x-1)

\newline

Answer:

y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as FOIL - First, Outer, Inner, Last). $\newline$ We need to multiply each term in the first binomial by each term in the second binomial. $\newline$ $y = -7(x + 9)(x - 1)$ $\newline$ $y = -7[(x \times x) + (x \times -1) + (9 \times x) + (9 \times -1)]$
Perform Multiplication: Perform the multiplication for each pair of terms. $\newline$ $y = -7[(x^2) - x + 9x - 9]$
Combine Like Terms: Combine like terms inside the brackets. $\newline$ y = $-7[x^2 + (9x - x) - 9]$ $\newline$ y = $-7[x^2 + 8x - 9]$
Distribute Coefficients: Distribute the $-7$ across each term inside the brackets. $\newline$ $y = -7(x^2) -7(8x) -7(-9)$ $\newline$ $y = -7x^2 - 56x + 63$
Write in Standard Form: Write the final expression in standard form, which is $ax^2 + bx + c$ . $\newline$ $y = -7x^2 - 56x + 63$ $\newline$ This is the standard form of the quadratic function.