At how many points does the graph of function below intercept the
x axis y=4x^2-9x+9?

a.2
b.1
c.0

C. 0

Step-by-step explanation:

The points of intercection between the graph of a quadratic function of the form are given by the discriminant of the quadratic formula.

Remember that the quadratic formula is:

The discriminant of he quadratic formula is just the thing inside the radical, in other words:

- If the discriminant is negative, the graph of the quadratic function doesn't intercept the x-axis.

- If the discriminant is positive, the graph of the quadratic function intercept the x-axis at 2 points.

- If the discriminant is 0, the graph of the quadratic function intercept the x-axis at 1 point.

We can infer form our quadratic that , , and , so let's replace the values in the discriminant:

Since the discriminant is negative, we can conclude that the graph of the quadratic function doesn't intercept the x-axis at any point.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

the answer is d

step-by-step explanation: