The equation of a parabola is y = x^2 + 8x + 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 square: Complete the square to transform the given equation into vertex form. The given equation is y = x^2 + 8x + 19. To complete the square, we need to find the value that makes x^2 + 8x into a perfect square trinomial. We do this by taking half of the coefficient of x, which is 8, dividing it by 2 to get 4, and then squaring it to get 16. We will add and subtract this value within the equation.Add and subtract: Add and subtract the value found in Step 2 to the equation. y = x^2 + 8x + 19 can be written as y = x^2 + 8x + 16 + 19 - 16, by adding and subtracting 16.Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. y = (x^2 + 8x + 16) + 19 - 16 simplifies to y = (x + 4)^2 + 3, since x^2 + 8x + 16 is a perfect square trinomial and 19 - 16 equals 3.

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The equation of a parabola is $y = x^2 + 8x + 19$ . 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 + 8x + 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 square: Complete the square to transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 + 8x + 19$ . To complete the square, we need to find the value that makes $x^2 + 8x$ into a perfect square trinomial. We do this by taking half of the coefficient of $x$ , which is $8$ , dividing it by $2$ to get $4$ , and then squaring it to get $16$ . We will add and subtract this value within the equation.
Add and subtract: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 + 8x + 19$ can be written as $y = x^2 + 8x + 16 + 19 - 16$ , by adding and subtracting $16$ .
Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $y = (x^2 + 8x + 16) + 19 - 16$ simplifies to $y = (x + 4)^2 + 3$ , since $x^2 + 8x + 16$ is a perfect square trinomial and $19 - 16$ equals $3$ .