The equation of a parabola is y = x^2 - 2x + 6. 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 equation in vertex form. We have the equation y = x^2 - 2x + 6. 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 -2, which is -1, and then square it to get 1. We will add and subtract this value inside the equation.Add Value Inside Equation: Add and subtract the value found in Step 2 inside the equation. y = x^2 - 2x + 1 + 6 - 1 We added and subtracted 1 to create a perfect square trinomial.Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. y = (x^2 - 2x + 1) + 6 - 1 y = (x - 1)^2 + 5 Now the equation is in vertex form, with the vertex at (1, 5).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

. 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. 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 equation in vertex form. $\newline$ We have the equation $y = x^2 - 2x + 6$ . 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 $-2$ , which is $-1$ , and then square it to get $1$ . We will add and subtract this value inside the equation.
Add Value Inside Equation: Add and subtract the value found in Step $2$ inside the equation. $\newline$ $y = x^2 - 2x + 1 + 6 - 1$ $\newline$ We added and subtracted $1$ to create a perfect square trinomial.
Rewrite Equation: Rewrite the equation with the perfect square trinomial and combine the constants. $\newline$ $y = (x^2 - 2x + 1) + 6 - 1$ $\newline$ $y = (x - 1)^2 + 5$ $\newline$ Now the equation is in vertex form, with the vertex at $(1, 5)$ .