The equation of a parabola is y = x^2 + 10x + 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 transform the given equation into vertex form. We have the equation y = x^2 + 10x + 19. To complete the square, we need to find the value that makes x^2 + 10x a perfect square trinomial. This value is (10/2)^2 = 25. We will add and subtract 25 inside the equation.Add and subtract: Add and subtract 25 to the equation. y = x^2 + 10x + 19 y = x^2 + 10x + 25 - 25 + 19 Now, we have added 25 and subtracted 25, which keeps the equation balanced.Group and combine: Group the perfect square trinomial and combine the constants. y = (x^2 + 10x + 25) - 25 + 19 y = (x + 5)^2 - 6 Now, we have the equation in vertex form, where (x + 5)^2 is the perfect square trinomial and -6 is the combination of the constants.

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The equation of a parabola is $y = x^2 + 10x + 19$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 + 10x + 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 transform the given equation into vertex form. $\newline$ We have the equation $y = x^2 + 10x + 19$ . To complete the square, we need to find the value that makes $x^2 + 10x$ a perfect square trinomial. This value is $(10/2)^2 = 25$ . We will add and subtract $25$ inside the equation.
Add and subtract: Add and subtract $25$ to the equation. $\newline$ $y = x^2 + 10x + 19$ $\newline$ $y = x^2 + 10x + 25 - 25 + 19$ $\newline$ Now, we have added $25$ and subtracted $25$ , which keeps the equation balanced.
Group and combine: Group the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 10x + 25) - 25 + 19$ $\newline$ $y = (x + 5)^2 - 6$ $\newline$ Now, we have the equation in vertex form, where $(x + 5)^2$ is the perfect square trinomial and $-6$ is the combination of the constants.