Question

How many x-intercepts does the graph of the given equation have?

Answer 1

The discriminant is b^2 - 4ac.
Find x-intercepts by setting y = 0 and solving for x.
With 0 = -4x^2 + 4x - 1, this implies that a = -4, b = 4, and c = -1.
               discriminant = 4^2 - 4(-4)(-1)
                                      = 16 - 16
                                      = 0
The discriminant of 0 means there is only one real solution to 0 = -4x^2 + 4x - 1.
So there is only one x-intercept.

Your answer is one x-intercept.

Answer 2

Use the formula x=b^2-4ac
a= -4 , b= 4 , c= -1
Plug in into your formula
(4)^2-4(-4*-1)
16-16
x=0
so the solution only has one x-intercept