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 y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete square: Complete the square to transform the given equation into vertex form. We have the equation y = x^2 + 6x + 6. To complete the square, we need to find the value that makes x^2 + 6x a perfect square trinomial. This value is (6/2)^2 = 3^2 = 9. We will add and subtract 9 to the equation.Add and subtract: Add and subtract the value found in Step 2 to the equation. y = x^2 + 6x + 9 - 9 + 6 Now, we can rewrite the equation as: y = (x^2 + 6x + 9) - 3Factor and simplify: Factor the perfect square trinomial and simplify the equation. The perfect square trinomial x^2 + 6x + 9 can be factored as (x + 3)^2. So, the equation becomes: y = (x + 3)^2 - 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 $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete square: Complete the square to transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 + 6x + 6$ . To complete the square, we need to find the value that makes $x^2 + 6x$ a perfect square trinomial. This value is $(\frac{6}{2})^2 = 3^2 = 9$ . We will add and subtract $9$ to the equation.
Add and subtract: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 6x + 9 - 9 + 6$ $\newline$ Now, we can rewrite the equation as: $\newline$ $y = (x^2 + 6x + 9) - 3$
Factor and simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ The perfect square trinomial $x^2 + 6x + 9$ can be factored as $(x + 3)^2$ . So, the equation becomes: $\newline$ $y = (x + 3)^2 - 3$