The equation of a parabola is y = x^2 + 8x + 18. 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 + 8x + 18. To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the x-terms.Calculate value: Calculate the value needed to complete the square. We take half of the coefficient of the x-term, which is 8, and square it to get (8/2)^2 = 4^2 = 16. This is the value we will add and subtract to complete the square.Rewrite equation: Rewrite the equation by adding and subtracting the value found in Step 3. y = x^2 + 8x + 16 + 18 - 16 y = (x^2 + 8x + 16) + 2 Now, the equation includes the perfect square trinomial (x^2 + 8x + 16) and the constant 2.Factor and simplify: Factor the perfect square trinomial and simplify the equation. y = (x + 4)^2 + 2 This is the vertex form of the given parabola, where the vertex is (-4, 2).

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The equation of a parabola is $y = x^2 + 8x + 18$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 2

Convert equations of parabolas from general to vertex form

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Q. The equation of a parabola is

y = x^2 + 8x + 18

. 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 $y = x^2 + 8x + 18$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial with the $x$ -terms.
Calculate value: Calculate the value needed to complete the square. $\newline$ We take half of the coefficient of the $x$ -term, which is $8$ , and square it to get $(\frac{8}{2})^2 = 4^2 = 16$ . This is the value we will add and subtract to complete the square.
Rewrite equation: Rewrite the equation by adding and subtracting the value found in Step $3$ . $\newline$ $y = x^2 + 8x + 16 + 18 - 16$ $\newline$ $y = (x^2 + 8x + 16) + 2$ $\newline$ Now, the equation includes the perfect square trinomial $(x^2 + 8x + 16)$ and the constant $2$ .
Factor and simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x + 4)^2 + 2$ $\newline$ This is the vertex form of the given parabola, where the vertex is $(-4, 2)$ .