The equation of a parabola is y = x^2 - 8x + 15. 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 the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete the square: Complete the square to rewrite the equation in vertex form. We start with the given equation y = x^2 - 8x + 15. 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.Add and subtract 16: Add and subtract 16 to the equation. y = x^2 - 8x + 16 - 16 + 15 Now we have the perfect square trinomial x^2 - 8x + 16 and the constants -16 and +15.Factor and combine constants: Factor the perfect square trinomial and combine the constants. y = (x - 4)^2 - 16 + 15 y = (x - 4)^2 - 1 Now the equation is in vertex form, with the vertex being (4, -1).

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The equation of a parabola is $y = x^2 - 8x + 15$ . 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 + 15

. 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. $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the square: Complete the square to rewrite the equation in vertex form. $\newline$ We start with the given equation $y = x^2 - 8x + 15$ . 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.
Add and subtract $16$ : Add and subtract $16$ to the equation. $y = x^2 - 8x + 16 - 16 + 15$ Now we have the perfect square trinomial $x^2 - 8x + 16$ and the constants $-16$ and $+15$ .
Factor and combine constants: Factor the perfect square trinomial and combine the constants. $\newline$ $y = (x - 4)^2 - 16 + 15$ $\newline$ $y = (x - 4)^2 - 1$ $\newline$ Now the equation is in vertex form, with the vertex being $(4, -1)$ .