Answer:
C. 0
Step-by-step explanation:
The points of intercection between the graph of a quadratic function of the form [tex]ax^{2} +bx+c[/tex] are given by the discriminant of the quadratic formula.
Remember that the quadratic formula is:
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac } }{2a}[/tex]
The discriminant of he quadratic formula is just the thing inside the radical, in other words:
[tex]discriminant=b^{2} -4ac[/tex]
- 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 [tex]a=4[/tex], [tex]b=-9[/tex], and [tex]c=9[/tex], so let's replace the values in the discriminant:
[tex]discriminant=b^{2} -4ac[/tex]
[tex]discriminant=(-9)^{2} -4(4)(9)[/tex]
[tex]discriminant=81-144[/tex]
[tex]discriminant=81-144[/tex]
[tex]discriminant=-63[/tex]
Since the discriminant is negative, we can conclude that the graph of the quadratic function doesn't intercept the x-axis at any point.
