The equation of a parabola is y = x^2 - 6x + 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 the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Consider Given Quadratic Equation: Consider the given quadratic equation y = x^2 - 6x + 19. We need to complete the square to rewrite this equation in vertex form.Find Square of Half: Find the square of half the coefficient of x. Half the coefficient of x is -6/2, which is -3. Squaring this gives us (-3)^2 = 9.Add/Subtract Square Inside: Add and subtract the square of half the coefficient of x inside the equation. y = x^2 - 6x + 9 - 9 + 19 We add 9 to complete the square and then subtract 9 to keep the equation balanced.Rewrite Equation by Grouping: Rewrite the equation by grouping the perfect square trinomial and combining the constants. y = (x^2 - 6x + 9) + (19 - 9) y = (x - 3)^2 + 10 Now the equation is in vertex form.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 - 6x + 19$ . 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 2

Convert equations of parabolas from general to vertex form

Full solution

Q. The equation of a parabola is

y = x^2 - 6x + 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 the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Consider Given Quadratic Equation: Consider the given quadratic equation $y = x^2 - 6x + 19$ . $\newline$ We need to complete the square to rewrite this equation in vertex form.
Find Square of Half: Find the square of half the coefficient of $x$ . Half the coefficient of $x$ is $-6/2$ , which is $-3$ . Squaring this gives us $(-3)^2 = 9$ .
Add/Subtract Square Inside: Add and subtract the square of half the coefficient of $x$ inside the equation. $\newline$ $y = x^2 - 6x + 9 - 9 + 19$ $\newline$ We add $9$ to complete the square and then subtract $9$ to keep the equation balanced.
Rewrite Equation by Grouping: Rewrite the equation by grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 6x + 9) + (19 - 9)$ $\newline$ $y = (x - 3)^2 + 10$ $\newline$ Now the equation is in vertex form.