The equation of a parabola is y = x^2 - 2x - 8. 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. The given equation is y = x^2 - 2x - 8. 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. The coefficient of x is -2, so we take half of it, which is -1, and then square it to get 1. We will add and subtract this value inside the equation. y = x^2 - 2x + 1 - 1 - 8Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 - 2x + 1) - 1 - 8 y = (x - 1)^2 - 9 Now the equation is in vertex form, where the vertex (h, k) is (1, -9).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 - 2x - 8$ . 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 - 2x - 8

. 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. $\newline$ The given equation is $y = x^2 - 2x - 8$ . 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. $\newline$ The coefficient of $x$ is $-2$ , so we take half of it, which is $-1$ , and then square it to get $1$ . We will add and subtract this value inside the equation. $\newline$ $y = x^2 - 2x + 1 - 1 - 8$
Rewrite equation: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 2x + 1) - 1 - 8$ $\newline$ $y = (x - 1)^2 - 9$ $\newline$ Now the equation is in vertex form, where the vertex $(h, k)$ is $(1, -9)$ .