The equation of a parabola is y = x^2 - 6x + 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 square transformation: Complete the square to transform the given equation into vertex form. The given equation is y = x^2 - 6x + 8. To complete the square, we need to find the value to add and subtract that will create a perfect square trinomial. We take the coefficient of x, which is -6, divide it by 2, and square it: (-6/2)^2 = (-3)^2 = 9. We will add and subtract 9 to the equation.Add/subtract value: Add and subtract the value found in Step 2 to the equation. y = x^2 - 6x + 9 - 9 + 8 Now we have the perfect square trinomial x^2 - 6x + 9 and the constants -9 + 8.Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. y = (x^2 - 6x + 9) - 1 The perfect square trinomial (x^2 - 6x + 9) can be factored into (x - 3)^2, and the constants -9 + 8 simplify to -1.Write in vertex form: Write the equation in vertex form. y = (x - 3)^2 - 1 This is the vertex form of the given parabola, where the vertex is (3, -1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 - 6x + 8$ . 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 - 6x + 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 square transformation: Complete the square to transform the given equation into vertex form. $\newline$ The given equation is $y = x^2 - 6x + 8$ . To complete the square, we need to find the value to add and subtract that will create a perfect square trinomial. We take the coefficient of $x$ , which is $-6$ , divide it by $2$ , and square it: $(-6/2)^2 = (-3)^2 = 9$ . We will add and subtract $9$ to the equation.
Add/subtract value: Add and subtract the value found in Step $2$ to the equation. $\newline$ $y = x^2 - 6x + 9 - 9 + 8$ $\newline$ Now we have the perfect square trinomial $x^2 - 6x + 9$ and the constants $-9 + 8$ .
Rewrite equation: Rewrite the equation grouping the perfect square trinomial and combining the constants. $\newline$ $y = (x^2 - 6x + 9) - 1$ $\newline$ The perfect square trinomial $(x^2 - 6x + 9)$ can be factored into $(x - 3)^2$ , and the constants $-9 + 8$ simplify to $-1$ .
Write in vertex form: Write the equation in vertex form. $\newline$ $y = (x - 3)^2 - 1$ $\newline$ This is the vertex form of the given parabola, where the vertex is $(3, -1)$ .