Re-write the quadratic function below in Standard Form y=-(x-5)^(2)+6 Answer: y=

Question Prompt: Question prompt: What is the standard form of the quadratic function y = -(x - 5)² + 6?Expand and Simplify: Expand the squared term in the quadratic function. To expand (x - 5)², we use the formula (a - b)² = a² - 2ab + b², where a = x and b = 5. (x - 5)² = x² - 2*x*5 + 5² = x² - 10x + 25Multiply by -1: Multiply the expanded term by -1, as indicated by the negative sign in front of the parentheses. -1 * (x² - 10x + 25) = -x² + 10x - 25Add Constant Term: Add the constant term 6 to the result from Step 2 to complete the quadratic function in standard form. y = -x² + 10x - 25 + 6Combine Like Terms: Combine like terms to simplify the quadratic function. y = -x² + 10x - 19

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

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y=-(x-5)^{2}+6

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Answer:

y=

Question Prompt: Question prompt: What is the standard form of the quadratic function $y = -(x - 5)^2 + 6$ ?
Expand and Simplify: Expand the squared term in the quadratic function. $\newline$ To expand $(x - 5)^2$ , we use the formula $(a - b)^2 = a^2 - 2ab + b^2$ , where $a = x$ and $b = 5$ . $\newline$ $(x - 5)^2 = x^2 - 2 \times x \times 5 + 5^2$ $\newline$ $= x^2 - 10x + 25$
Multiply by $-1$ : Multiply the expanded term by $-1$ , as indicated by the negative sign in front of the parentheses. $\newline$ $-1 \times (x^2 - 10x + 25) = -x^2 + 10x - 25$
Add Constant Term: Add the constant term $6$ to the result from Step $2$ to complete the quadratic function in standard form. $\newline$ $y = -x^2 + 10x - 25 + 6$
Combine Like Terms: Combine like terms to simplify the quadratic function. $\newline$ $y = -x^2 + 10x - 19$