How do you go about finding the roots\x intercepts of the function; 2x^2-16x+36 so that I can graph it ?

Question

Thank you !

Answer 1

First, divide by 2.
x^2-8x+18 = 0

the roots are provided by the quadratic formula:

x = (8±√(8^2-(4*1*18))/2

You can see that they are complex because the discriminant is negative. So, there are no x-intercepts.

The y-intercept is of course 36, since there, x=0.

To find the vertex, complete the square.

y = 2x^2-16x+26
= 2(x^2-8x) + 36
= 2(x^2-8x+16) + 36 - 2*16
= 2(x-4)^2 + 4

So, the vertex is at (2,4)

Now you should be able to sketch it, using symmetry around the line x=2.