# What is the vertex form of y= x^2 - 5x + 4 ?

Vertex form ${\left(x - \frac{5}{2}\right)}^{2} = y - - \frac{9}{4}$

#### Explanation:

from the given $y = {x}^{2} - 5 x + 4$
we complete the square

$y = {x}^{2} - 5 x + \frac{25}{4} - \frac{25}{4} + 4$

$y = \left({x}^{2} - 5 x + \frac{25}{4}\right) - \frac{25}{4} + \frac{16}{4}$

$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{9}{4}$

$y + \frac{9}{4} = {\left(x - \frac{5}{2}\right)}^{2}$

also

${\left(x - \frac{5}{2}\right)}^{2} = y - - \frac{9}{4}$

graph{y=x^2-5x+4[-20,20,-10,10]}

have a nice day!