The equation of a parabola is y = x^2 + 8x + 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 square: Complete the square to rewrite the given equation in vertex form. The given equation is y = x^2 + 8x + 12. To complete the square, we need to find the value that makes x^2 + 8x into a perfect square trinomial. This value is (8/2)^2 = 4^2 = 16. We will add and subtract 16 within the equation.Add and subtract: Add and subtract 16 to the equation. y = x^2 + 8x + 12 can be written as y = x^2 + 8x + 16 - 16 + 12 by adding and subtracting 16.Group terms, combine: Group the perfect square trinomial and combine the constants. Now, we group the terms to form a perfect square trinomial and combine the constants: y = (x^2 + 8x + 16) - 16 + 12.Factor trinomial, simplify: Factor the perfect square trinomial and simplify the constant term. The factored form of the perfect square trinomial is (x + 4)^2, and combining the constants -16 + 12 gives -4. So, the equation becomes y = (x + 4)^2 - 4.

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The equation of a parabola is $y = x^2 + 8x + 12$ . 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 + 8x + 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. $\newline$ 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 rewrite the given equation in vertex form. $\newline$ The given equation is $y = x^2 + 8x + 12$ . To complete the square, we need to find the value that makes $x^2 + 8x$ into a perfect square trinomial. This value is $(8/2)^2 = 4^2 = 16$ . We will add and subtract $16$ within the equation.
Add and subtract: Add and subtract $16$ to the equation. $y = x^2 + 8x + 12$ can be written as $y = x^2 + 8x + 16 - 16 + 12$ by adding and subtracting $16$ .
Group terms, combine: Group the perfect square trinomial and combine the constants. $\newline$ Now, we group the terms to form a perfect square trinomial and combine the constants: $y = (x^2 + 8x + 16) - 16 + 12$ .
Factor trinomial, simplify: Factor the perfect square trinomial and simplify the constant term. $\newline$ The factored form of the perfect square trinomial is $(x + 4)^2$ , and combining the constants $-16 + 12$ gives $-4$ . So, the equation becomes $y = (x + 4)^2 - 4$ .