The equation of a parabola is y = x^2 + 8x + 11. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Understanding vertex form: Understand 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.Completing the square: Complete the square to transform the given equation into vertex form. We have y = x^2 + 8x + 11. To complete the square, we need to add and subtract (8/2)^2, which is 16, inside the x terms. y = x^2 + 8x + 16 - 16 + 11Factoring and simplifying: Factor the perfect square trinomial and simplify the constant terms. y = (x^2 + 8x + 16) - 16 + 11 y = (x + 4)^2 - 5

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 + 8x + 11$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

View step-by-step help

Home

Math Problems

Algebra 1

Write a quadratic function in vertex form

Full solution

Q. The equation of a parabola is

y = x^2 + 8x + 11

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Understanding vertex form: Understand 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.
Completing the square: Complete the square to transform the given equation into vertex form. $\newline$ We have $y = x^2 + 8x + 11$ . To complete the square, we need to add and subtract $\left(\frac{8}{2}\right)^2$ , which is $16$ , inside the x terms. $\newline$ $y = x^2 + 8x + 16 - 16 + 11$
Factoring and simplifying: Factor the perfect square trinomial and simplify the constant terms. $\newline$ y = $(x^2 + 8x + 16) - 16 + 11$ $\newline$ y = $(x + 4)^2 - 5$