Answer:
The correct graph is D.
Step-by-step explanation:
Given a quadratic equation :
[tex]y=ax^{2}+bx+c[/tex]
You can find the roots (where the graph intersects the x-axis) applying the following equation :
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
and
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
We define the discriminant as [tex]b^{2}-4ac[/tex]
If [tex]b^{2}-4ac>0[/tex] then the graph will intersect the x-axis in two points
If [tex]b^{2}-4ac=0[/tex] then the graph will intersect the x-axis in one point.
Finally, If [tex]b^{2}-4ac<0[/tex] then the graph won't intersect the x-axis because it will not have real roots.
In this exercise, the graph that doesn't intersect the x-axis is graph D.
