Re-write the quadratic function below in Standard Form y=-9(x-2)(x-5) Answer: y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as the FOIL method for binomials). We need to multiply each term in the first binomial by each term in the second binomial. y = -9(x - 2)(x - 5) y = -9[(x * x) + (x * -5) + (-2 * x) + (-2 * -5)]Perform Multiplication of Terms: Perform the multiplication for each pair of terms. y = -9[(x^2) + (-5x) + (-2x) + 10] Combine like terms within the brackets. y = -9[x^2 - 5x - 2x + 10] y = -9[x^2 - 7x + 10]Distribute Coefficients: Distribute the -9 to each term inside the brackets. y = -9 * x^2 + 9 * 7x - 9 * 10 y = -9x^2 + 63x - 90Write in Standard Form: Write the quadratic function in Standard Form, which is y = ax^2 + bx + c. The function is now in Standard Form. y = -9x^2 + 63x - 90

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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=-9(x-2)(x-5)

\newline

Answer:

y=

Expand Quadratic Function: Expand the quadratic function using the distributive property (also known as the FOIL method for binomials). $\newline$ We need to multiply each term in the first binomial by each term in the second binomial. $\newline$ $y = -9(x - 2)(x - 5)$ $\newline$ $y = -9[(x \times x) + (x \times -5) + (-2 \times x) + (-2 \times -5)]$
Perform Multiplication of Terms: Perform the multiplication for each pair of terms. $\newline$ $y = -9[(x^2) + (-5x) + (-2x) + 10]$ $\newline$ Combine like terms within the brackets. $\newline$ $y = -9[x^2 - 5x - 2x + 10]$ $\newline$ $y = -9[x^2 - 7x + 10]$
Distribute Coefficients: Distribute the $-9$ to each term inside the brackets. $\newline$ $y = -9 \times x^2 + 9 \times 7x - 9 \times 10$ $\newline$ $y = -9x^2 + 63x - 90$
Write in Standard Form: Write the quadratic function in Standard Form, which is $y = ax^2 + bx + c$ . $\newline$ The function is now in Standard Form. $\newline$ $y = -9x^2 + 63x - 90$