Question

Y=x2 - 5x + 8
Write each equation in vertex form

Answer 1

Hello!

`\large\boxed{y = (x - (5)/(2))^(2) + (7)/(4)}`

y = x² - 5x + 8

Rewrite in vertex form by completing the square.

We can use the "a" and "b" terms to rewrite as a square binomial:

y = (x² - 5x) + 8

Since b = 5, then the second term of the square binomial will be half, or 5/2, like so:

(x - 5/2)²

Squaring the second term gives 25/4, so we must subtract this from the equation to cancel it out:

y = (x - 5/2)² + 8 - 25/4

Simplify using a common denominator:

y = (x - 5/2)² + 32/4 - 25/4

y = (x - 5/2)² + 7/4

The vertex of this equation is at (5/2, 7/4), or (2.5, 1.25).