The equation of a parabola is y = x^2 - 8x + 17. 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.Given Quadratic Equation: Consider the given quadratic equation y = x^2 - 8x + 17. We need to complete the square to transform this equation into vertex form.Find Square of Half: Find the square of half the coefficient of x. The coefficient of x is -8. Half of this coefficient is -8/2 = -4. Squaring this value gives (-4)^2 = 16.Rewrite Quadratic Equation: Rewrite the quadratic equation by adding and subtracting the square of half the coefficient of x. y = x^2 - 8x + 16 + 17 - 16 y = (x^2 - 8x + 16) + 1Recognize Perfect Square Trinomial: Recognize the perfect square trinomial and factor it. y = (x - 4)^2 + 1 This is now in vertex form, where (h, k) = (4, 1).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a parabola is $y = x^2 - 8x + 17$ . 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 - 8x + 17

. 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.
Given Quadratic Equation: Consider the given quadratic equation $y = x^2 - 8x + 17$ . $\newline$ We need to complete the square to transform this equation into vertex form.
Find Square of Half: Find the square of half the coefficient of $x$ . The coefficient of $x$ is $-8$ . Half of this coefficient is $-8/2 = -4$ . Squaring this value gives $(-4)^2 = 16$ .
Rewrite Quadratic Equation: Rewrite the quadratic equation by adding and subtracting the square of half the coefficient of $x$ . $y = x^2 - 8x + 16 + 17 - 16$ $y = (x^2 - 8x + 16) + 1$
Recognize Perfect Square Trinomial: Recognize the perfect square trinomial and factor it. $\newline$ $y = (x - 4)^2 + 1$ $\newline$ This is now in vertex form, where $(h, k) = (4, 1)$ .