The equation of a parabola is y = x^2 - 8x + 7. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete Square Transformation: Complete the square to transform the given equation into vertex form. We start with the given equation y = x^2 - 8x + 7. To complete the square, we need to find the value that makes x^2 - 8x a perfect square trinomial. We do this by taking half of the coefficient of x, squaring it, and adding it to and subtracting it from the equation. Half of -8 is -4, and (-4)^2 = 16. So we add and subtract 16 to the equation. y = x^2 - 8x + 16 - 16 + 7Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. Now we have y = (x^2 - 8x + 16) - 16 + 7. The expression in the parentheses is a perfect square trinomial, which can be written as (x - 4)^2. So the equation becomes y = (x - 4)^2 - 16 + 7. Simplifying the constants gives us y = (x - 4)^2 - 9.

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The equation of a parabola is $y = x^2 - 8x + 7$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 8x + 7

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Identify Vertex Form: Identify the vertex form of a parabola. The vertex form of a parabola is given by $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete Square Transformation: Complete the square to transform the given equation into vertex form. $\newline$ We start with the given equation $y = x^2 - 8x + 7$ . To complete the square, we need to find the value that makes $x^2 - 8x$ a perfect square trinomial. We do this by taking half of the coefficient of $x$ , squaring it, and adding it to and subtracting it from the equation. $\newline$ Half of $-8$ is $-4$ , and $(-4)^2 = 16$ . So we add and subtract $16$ to the equation. $\newline$ $y = x^2 - 8x + 16 - 16 + 7$
Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. $\newline$ Now we have $y = (x^2 - 8x + 16) - 16 + 7$ . The expression in the parentheses is a perfect square trinomial, which can be written as $(x - 4)^2$ . $\newline$ So the equation becomes $y = (x - 4)^2 - 16 + 7$ . $\newline$ Simplifying the constants gives us $y = (x - 4)^2 - 9$ .