F(x) = -4x(2)+ 12x – 9
What is the value of the discriminant of f?
How many x-intercepts does the graph of f have?

For this case we have the following function:

we have:

Where:

By definition, the discriminant of a quadratic equation is given by:

Two different real roots

Two equal real roots

: Two different complex roots

Substituting the values we have:

We have two equal real roots.

To find the intersections with the x axis, we do

We apply the quadratic formula:

Substituting the values we have:

The intersection with the x axis is

The intersection with the x axis is

Part A) The value of the discriminant of f is zero

Part B) The quadratic equation has only one x-intercept

Step-by-step explanation:

Part A) What is the value of the discriminant of f?

we know that

In a quadratic equation of the form

the discriminant is equal to

in this problem we have

so

substitute

Part B) How many x-intercepts does the graph of f have?

we know that

In a quadratic equation

If the discriminant D is equal to zero, then the equation has only one real solution

That means

The quadratic equation has only one x-intercept