which is the graph of a quadratic equation that has a positive discriminant?

Explanation:

Step1: Recall discriminant property

For a quadratic equation (y = ax^{2}+bx + c), the discriminant (\Delta=b^{2}-4ac). When (\Delta> 0), the quadratic equation has two distinct real - roots.

Step2: Analyze graph - root relationship

The roots of a quadratic equation (y = ax^{2}+bx + c) are the (x) - intercepts of its graph. A quadratic equation with two distinct real roots will cross the (x) - axis at two different points.

Step3: Check the given graph

The given graph touches the (x) - axis at one point, which means it has a discriminant of (0) (since there is one real root). A graph of a quadratic equation with a positive discriminant should cross the (x) - axis at two distinct points. Since the provided graph does not meet this criterion, no answer can be given based on the single graph shown. But in general, the graph of a quadratic with a positive discriminant will cross the (x) - axis at two different points.

Answer:

The graph is not shown (the provided graph has discriminant = 0, not positive). A correct graph would cross the (x) - axis at two distinct points.