Hello!
[tex]\large\boxed{y = (x - \frac{5}{2})^{2} + \frac{7}{4}}[/tex]
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).
