The equation of a parabola is y = x^2 - 6x + 6. 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 given equation in vertex form. The given equation is y = x^2 - 6x + 6. To complete the square, we need to find the value that makes x^2 - 6x a perfect square trinomial. We do this by taking half of the coefficient of x, which is -6, dividing it by 2 to get -3, and then squaring it to get 9. We will add and subtract this value inside the equation.Add and subtract values: Add and subtract the value found in Step 2 inside the equation. y = x^2 - 6x + 9 - 9 + 6 Now we have added 9 and subtracted 9, which keeps the equation balanced.Group and combine: Group the perfect square trinomial and combine the constants. y = (x^2 - 6x + 9) - 9 + 6 y = (x - 3)^2 - 3 Now we have the equation in vertex form, where the vertex is (3, -3).

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The equation of a parabola is $y = x^2 - 6x + 6$ . 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 - 6x + 6

. 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 given equation in vertex form. $\newline$ The given equation is $y = x^2 - 6x + 6$ . To complete the square, we need to find the value that makes $x^2 - 6x$ a perfect square trinomial. We do this by taking half of the coefficient of $x$ , which is $-6$ , dividing it by $2$ to get $-3$ , and then squaring it to get $9$ . We will add and subtract this value inside the equation.
Add and subtract values: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 - 6x + 9 - 9 + 6$ $\newline$ Now we have added $9$ and subtracted $9$ , which keeps the equation balanced.
Group and combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 6x + 9) - 9 + 6$ $\newline$ $y = (x - 3)^2 - 3$ $\newline$ Now we have the equation in vertex form, where the vertex is $(3, -3)$ .