The equation of a parabola is y = x^2 + 6x + 19. 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 + 6x + 19. To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial.Calculate value: Calculate the value needed to complete the square. We take the coefficient of the x term, which is 6, divide it by 2, and then square it to get the value to add and subtract. (6/2)^2 = 3^2 = 9Add and subtract: Add and subtract the calculated value inside the equation. y = x^2 + 6x + 9 + 19 - 9 y = (x^2 + 6x + 9) + 10 Now, the equation has a perfect square trinomial and a constant term.Factor and simplify: Factor the perfect square trinomial and simplify the equation. y = (x + 3)^2 + 10 This is the equation in vertex form, where the vertex is (-3, 10).

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The equation of a parabola is $y = x^2 + 6x + 19$ . 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 + 6x + 19

. 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 the square: Complete the square to rewrite the given equation in vertex form. $\newline$ The given equation is $y = x^2 + 6x + 19$ . To complete the square, we need to find a value that, when added and subtracted to the equation, forms a perfect square trinomial.
Calculate value: Calculate the value needed to complete the square. $\newline$ We take the coefficient of the $x$ term, which is $6$ , divide it by $2$ , and then square it to get the value to add and subtract. $\newline$ $(\frac{6}{2})^2 = 3^2 = 9$
Add and subtract: Add and subtract the calculated value inside the equation. $\newline$ $y = x^2 + 6x + 9 + 19 - 9$ $\newline$ $y = (x^2 + 6x + 9) + 10$ $\newline$ Now, the equation has a perfect square trinomial and a constant term $10$ .
Factor and simplify: Factor the perfect square trinomial and simplify the equation. $\newline$ $y = (x + 3)^2 + 10$ $\newline$ This is the equation in vertex form, where the vertex is $(-3, 10)$ .