The equation of a parabola is y = x^2 - 10x + 22. 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 - 10x + 22. To complete the square, we need to find the value that makes x^2 - 10x a perfect square trinomial. This value is given by (10/2)^2 = 25. We will add and subtract 25 inside the equation.Add and Subtract 25: Add and subtract 25 to the equation. y = x^2 - 10x + 22 y = x^2 - 10x + 25 - 25 + 22 Now, we have added 25 and subtracted 25, which keeps the equation balanced.Group and Combine: Group the perfect square trinomial and combine the constants. y = (x^2 - 10x + 25) - 25 + 22 y = (x - 5)^2 - 3 Now, the equation is in vertex form, where (x - 5)^2 is the perfect square trinomial and -3 is the combination of the constants.

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The equation of a parabola is $y = x^2 - 10x + 22$ . 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 - 10x + 22

. 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 the Square: Complete the square to rewrite the equation in vertex form. $\newline$ We have the equation $y = x^2 - 10x + 22$ . To complete the square, we need to find the value that makes $x^2 - 10x$ a perfect square trinomial. This value is given by $(10/2)^2 = 25$ . We will add and subtract $25$ inside the equation.
Add and Subtract $25$ : Add and subtract $25$ to the equation. $\newline$ $y = x^2 - 10x + 22$ $\newline$ $y = x^2 - 10x + 25 - 25 + 22$ $\newline$ Now, we have added $25$ and subtracted $25$ , which keeps the equation balanced.
Group and Combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 10x + 25) - 25 + 22$ $\newline$ $y = (x - 5)^2 - 3$ $\newline$ Now, the equation is in vertex form, where $(x - 5)^2$ is the perfect square trinomial and $-3$ is the combination of the constants.