Question

Which is the graph of a quadratic equation that has a negative discriminant?

Answer 1

Answer:

The correct graph is D.

Step-by-step explanation:

Given a quadratic equation :

$y=ax^{2}+bx+c$

You can find the roots (where the graph intersects the x-axis) applying the following equation :

$x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}$

and

$x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}$

We define the discriminant as $b^{2}-4ac$

If $b^{2}-4ac>0$ then the graph will intersect the x-axis in two points

If $b^{2}-4ac=0$ then the graph will intersect the x-axis in one point.

Finally, If $b^{2}-4ac$ 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.

Answer 2

Answer:

D

Step-by-step explanation:

A negative discriminant indicates that the quadratic equation has no real roots.

Thus the graph does not touch or intersect the x- axis

The only graph that does not touch or intersect the x- axis is the fourth one