which graph shows a quadratic function with a discriminant value of 0?

Explanation:

Step1: Recall discriminant - root relationship

For a quadratic function (y = ax^{2}+bx + c), the discriminant is (\Delta=b^{2}-4ac). When (\Delta = 0), the quadratic function has exactly one real - root.

Step2: Recall the relationship between roots and x - intercepts

The roots of a quadratic function (y = ax^{2}+bx + c) are the x - values where (y = 0). Geometrically, the roots are the x - intercepts of the graph of the quadratic function. So, a quadratic function with (\Delta=0) has exactly one x - intercept.

Step3: Analyze the graphs

Examine each graph. The first graph has two x - intercepts, the second graph has two x - intercepts, the third graph has one x - intercept, and the fourth graph has two x - intercepts.

Answer:

The third graph (from the left)