The equation of a parabola is y = x^2 + 8x + 17. 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. The given equation is y = x^2 + 8x + 17. To complete the square, we need to find the value that makes x^2 + 8x a perfect square trinomial. This value is (8/2)^2 = 4^2 = 16. We will add and subtract 16 inside the equation.Add and Subtract 16: Add and subtract 16 to the equation. y = x^2 + 8x + 17 y = x^2 + 8x + 16 + 17 - 16 Now, we have added 16 and subtracted 16, which keeps the equation balanced.Rewrite Equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 + 8x + 16) + 17 - 16 y = (x + 4)^2 + 1 Now, the equation is in vertex form, where (x + 4)^2 is the perfect square trinomial and 1 is the combined constant.

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The equation of a parabola is $y = x^2 + 8x + 17$ . 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 + 17

. 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. $\newline$ The given equation is $y = x^2 + 8x + 17$ . To complete the square, we need to find the value that makes $x^2 + 8x$ a perfect square trinomial. This value is $(\frac{8}{2})^2 = 4^2 = 16$ . We will add and subtract $16$ inside the equation.
Add and Subtract $16$ : Add and subtract $16$ to the equation. $\newline$ $y = x^2 + 8x + 17$ $\newline$ $y = x^2 + 8x + 16 + 17 - 16$ $\newline$ Now, we have added $16$ and subtracted $16$ , which keeps the equation balanced.
Rewrite Equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 + 8x + 16) + 17 - 16$ $\newline$ $y = (x + 4)^2 + 1$ $\newline$ Now, the equation is in vertex form, where $(x + 4)^2$ is the perfect square trinomial and $1$ is the combined constant.