The equation of a parabola is y = x^2 - 8x + 13. 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 the square: Complete the square to rewrite the equation in vertex form. We have the equation y = x^2 - 8x + 13. 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 this value inside the equation.Add and subtract value: Add and subtract the value found in Step 2 to the equation. y = x^2 - 8x + 16 - 16 + 13 We added 16 to complete the square and then subtracted 16 to keep the equation balanced.Group and combine: Group the perfect square trinomial and combine the constants. y = (x^2 - 8x + 16) - 16 + 13 y = (x - 4)^2 - 3 Now the equation is in vertex form, where (x - 4)^2 is the perfect square trinomial and -3 is the combination of the constants.

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The equation of a parabola is $y = x^2 - 8x + 13$ . 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 + 13

. 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the square: Complete the square to rewrite the equation in vertex form. $\newline$ We have the equation $y = x^2 - 8x + 13$ . 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 this value inside the equation.
Add and subtract value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 - 8x + 16 - 16 + 13$ $\newline$ We added $16$ to complete the square and then subtracted $16$ to keep the equation balanced.
Group and combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 8x + 16) - 16 + 13$ $\newline$ $y = (x - 4)^2 - 3$ $\newline$ Now the equation is in vertex form, where $(x - 4)^2$ is the perfect square trinomial and $-3$ is the combination of the constants.