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Complete the square to re-write the quadratic function in vertex form:

y=x^(2)-6x-7
Answer:
y=

Complete the square to re-write the quadratic function in vertex form: $\newline$ $y=x^{2}-6 x-7$ $\newline$ Answer: $y=$

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Write a quadratic function in vertex form

Full solution

Q. Complete the square to re-write the quadratic function in vertex form:

\newline

y=x^{2}-6 x-7

\newline

Answer:

y=

Identify Coefficients: Identify the quadratic and linear coefficients from the given quadratic equation. $\newline$ The quadratic equation is $y = x^2 - 6x - 7$ . The coefficient of $x^2$ (the quadratic coefficient) is $1$ , and the coefficient of $x$ (the linear coefficient) is $-6$ .
Calculate $(b/2)^2$ : Calculate the value of $(b/2)^2$ to complete the square. $\newline$ The linear coefficient $b$ is $-6$ . To complete the square, we need to add and subtract $(b/2)^2$ . $\newline$ $(b/2)^2 = (-6/2)^2 = (-3)^2 = 9$
Add/Subtract $(b/2)^2$ : Add and subtract $(b/2)^2$ inside the equation. $\newline$ We will add $9$ and subtract $9$ immediately after to keep the equation balanced. $\newline$ $y = x^2 - 6x + 9 - 9 - 7$
Group Trinomial & Constants: Group the perfect square trinomial and the constants. $\newline$ The perfect square trinomial is $x^2 - 6x + 9$ , and the constants are $-9 - 7$ . $\newline$ $y = (x^2 - 6x + 9) - 9 - 7$
Factor Trinomial: Factor the perfect square trinomial. $\newline$ The perfect square trinomial $x^2 - 6x + 9$ factors into $(x - 3)^2$ . $\newline$ $y = (x - 3)^2 - 9 - 7$
Combine Constants: Combine the constants to simplify the equation. $\newline$ Combine $-9$ and $-7$ to get $-16$ . $\newline$ $y = (x - 3)^2 - 16$

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