The equation of a parabola is y = x^2 + 8x + 16. 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 given equation in vertex form. The given equation is y = x^2 + 8x + 16. To complete the square, we need to find a value that makes x^2 + 8x a perfect square trinomial. The value to add and subtract is (8/2)^2 = 4^2 = 16. However, since 16 is already present in the equation, we do not need to add or subtract anything further.Rewrite by Factoring: Rewrite the equation by factoring the perfect square trinomial. The equation y = x^2 + 8x + 16 can be rewritten as y = (x + 4)^2 because x^2 + 8x + 16 is already a perfect square trinomial equivalent to (x + 4)^2.Final Equation in Vertex Form: Write the final equation in vertex form. The equation in vertex form is y = (x + 4)^2. This is because the equation y = x^2 + 8x + 16 is equivalent to y = (x + 4)^2, which is already in vertex form with a vertex at (-4, 0).

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The equation of a parabola is $y = x^2 + 8x + 16$ . 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 + 16

. 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 given equation in vertex form. The given equation is $y = x^2 + 8x + 16$ . To complete the square, we need to find a value that makes $x^2 + 8x$ a perfect square trinomial. The value to add and subtract is $(8/2)^2 = 4^2 = 16$ . However, since $16$ is already present in the equation, we do not need to add or subtract anything further.
Rewrite by Factoring: Rewrite the equation by factoring the perfect square trinomial. $\newline$ The equation $y = x^2 + 8x + 16$ can be rewritten as $y = (x + 4)^2$ because $x^2 + 8x + 16$ is already a perfect square trinomial equivalent to $(x + 4)^2$ .
Final Equation in Vertex Form: Write the final equation in vertex form. $\newline$ The equation in vertex form is $y = (x + 4)^2$ . This is because the equation $y = x^2 + 8x + 16$ is equivalent to $y = (x + 4)^2$ , which is already in vertex form with a vertex at $(-4, 0)$ .