Question

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

Answer 1

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

Explanation:

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