based on the graph, what could be the value of the discriminant?

Explanation:

Step1: Recall discriminant - root relationship

For a quadratic equation (y = ax^{2}+bx + c), the discriminant is (\Delta=b^{2}-4ac). If (\Delta> 0), the quadratic has two distinct real roots (the graph intersects the (x -)axis at two points). If (\Delta = 0), the quadratic has one real root (the graph touches the (x -)axis at one point). If (\Delta<0), the quadratic has no real roots (the graph does not intersect the (x -)axis).

Step2: Analyze the graph

The given graph of the quadratic function touches the (x -)axis at exactly one point. This means the quadratic equation (ax^{2}+bx + c = 0) has one real root.

Answer:

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