The equation of a parabola is y = x^2 + 2x + 7. 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 + 7. To complete the square, we need to add and subtract the square of half the coefficient of x inside the parentheses. The coefficient of x is 2, so half of it is 1, and squaring it gives us 1^2 = 1. We add and subtract 1 to complete the square. y = x^2 + 2x + 1 + 7 - 1Group and simplify: Group the perfect square trinomial and simplify the constant terms. Now we group the terms to form a perfect square trinomial and combine the constants. y = (x^2 + 2x + 1) + 7 - 1 y = (x + 1)^2 + 6Write in vertex form: Write the equation in vertex form. The equation in vertex form is now y = (x + 1)^2 + 6, where the vertex (h, k) is (-1, 6).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 + 2x + 7$ . 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 + 7

. 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 rewrite the equation in vertex form. $\newline$ We have the equation $y = x^2 + 2x + 7$ . To complete the square, we need to add and subtract the square of half the coefficient of $x$ inside the parentheses. $\newline$ The coefficient of $x$ is $2$ , so half of it is $1$ , and squaring it gives us $1^2 = 1$ . We add and subtract $1$ to complete the square. $\newline$ $y = x^2 + 2x + 1 + 7 - 1$
Group and simplify: Group the perfect square trinomial and simplify the constant terms. $\newline$ Now we group the terms to form a perfect square trinomial and combine the constants. $\newline$ $y = (x^2 + 2x + 1) + 7 - 1$ $\newline$ $y = (x + 1)^2 + 6$
Write in vertex form: Write the equation in vertex form. $\newline$ The equation in vertex form is now $y = (x + 1)^2 + 6$ , where the vertex $(h, k)$ is $(-1, 6)$ .