# How do you identify the important parts of y = x^2 -5x + 4 to graph it?

Sep 30, 2015

How to graph y = x^2 - 5x + 4

#### Explanation:

Here are the important parts to graph the quadratic function:
$y = {x}^{2} - 5 x + 4$
x-coordinate of vertex: $x = \left(- \frac{b}{2} a\right) = \frac{5}{2}$
y-coordinate of vertex:
$y = f \left(\frac{5}{2}\right) = \frac{25}{4} - \frac{25}{2} + 4 = - \frac{25}{4} + \frac{16}{4} = - \frac{9}{4}$
y-intercept--> Make x = 0 --> y = 4
x-intercepts --> make y = 0 --> solve ${x}^{2} - 5 x + 4 = 0$
Since (a + b = c = 0), use the Shortcut. The 2 real roots are:
x = 1 and $x = \frac{c}{a} = 4.$
graph{x^2 -5x + 4 [-10, 10, -5, 5]}