Re-write the quadratic function below in Standard Form y=-6(x+1)(x-6) Answer: y=

Multiply First Terms: We will multiply the first terms of each binomial together: x * x = x^2.Multiply Outer Terms: Next, we will multiply the outer terms: x * (-6) = -6x.Multiply Inner Terms: Then, we will multiply the inner terms: 1 * x = x.Multiply Last Terms: Finally, we will multiply the last terms of each binomial together: 1 * (-6) = -6.Combine Products: Now, we combine the products to get the expanded form: x^2 - 6x + x - 6.Combine Like Terms: We then combine like terms: x^2 - 6x + x - 6 = x^2 - 5x - 6.Multiply Entire Expression: Now, we need to multiply the entire expression by -6 to get the standard form of the quadratic function: y = -6(x^2 - 5x - 6).Distribute -6: Distribute -6 to each term inside the parentheses: y = -6 * x^2 + 6 * 5x + 6 * 6.Simplify Expression: Simplify the expression: y = -6x^2 + 30x + 36. This is the quadratic function in standard form.

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

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y=-6(x+1)(x-6)

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Answer:

y=

Multiply First Terms: We will multiply the first terms of each binomial together: $x \times x = x^2$ .
Multiply Outer Terms: Next, we will multiply the outer terms: $x \times (-6) = -6x$ .
Multiply Inner Terms: Then, we will multiply the inner terms: $1 \times x = x$ .
Multiply Last Terms: Finally, we will multiply the last terms of each binomial together: $1 \times (-6) = -6$ .
Combine Products: Now, we combine the products to get the expanded form: $x^2 - 6x + x - 6$ .
Combine Like Terms: We then combine like terms: $x^2 - 6x + x - 6 = x^2 - 5x - 6$ .
Multiply Entire Expression: Now, we need to multiply the entire expression by $-6$ to get the standard form of the quadratic function: $y = -6(x^2 - 5x - 6)$ .
Distribute $-6$ : Distribute $-6$ to each term inside the parentheses: $y = -6 \times x^2 + 6 \times 5x + 6 \times 6$ .
Simplify Expression: Simplify the expression: $y = -6x^2 + 30x + 36$ . This is the quadratic function in standard form.