which is the graph of a quadratic equation that has a negative 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 no real - roots. The graph of a quadratic function (y = ax^{2}+bx + c) is a parabola, and the (x) - intercepts of the graph are the real roots of the equation (ax^{2}+bx + c = 0). So, a quadratic equation with a negative discriminant has a parabola that does not cross the (x) - axis.

Step2: Analyze the given graph

The provided graph is a parabola that does not intersect the (x) - axis. Since the parabola does not cross the (x) - axis, the quadratic equation corresponding to this parabola has no real roots, which means its discriminant is negative.

Answer:

The given graph is the graph of a quadratic equation that has a negative discriminant.