The equation of a parabola is y = x^2 + 6x + 12. 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 transform the given equation into vertex form. The given equation is y = x^2 + 6x + 12. To complete the square, we need to find the value that makes x^2 + 6x into a perfect square trinomial. We do this by taking half of the coefficient of x, which is 6/2 = 3, and squaring it to get 9. We then add and subtract this value inside the equation. y = x^2 + 6x + 9 - 9 + 12Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. Now we have y = (x^2 + 6x + 9) - 9 + 12, which simplifies to y = (x + 3)^2 + 3.

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The equation of a parabola is $y = x^2 + 6x + 12$ . 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 + 12

. 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 transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 + 6x + 12$ . To complete the square, we need to find the value that makes $x^2 + 6x$ into a perfect square trinomial. We do this by taking half of the coefficient of $x$ , which is $\frac{6}{2} = 3$ , and squaring it to get $9$ . We then add and subtract this value inside the equation. $\newline$ $y = x^2 + 6x + 9 - 9 + 12$
Rewrite and Simplify: Rewrite the equation with the perfect square trinomial and simplify. $\newline$ Now we have $y = (x^2 + 6x + 9) - 9 + 12$ , which simplifies to $y = (x + 3)^2 + 3$ .