Question

what is the value of the discriminant of the equation graphed below? graph of a parabola with vertex on the horizontal line above the x - axis options: 0, -8, 3, 2

Explanation:

Step1: Recall discriminant - graph relation

For a quadratic function \( y = ax^2+bx + c \), the discriminant is \( D=b^2 - 4ac \). The graph of a quadratic is a parabola. If the parabola touches the x - axis at exactly one point (a repeated root), the discriminant is 0. If it intersects the x - axis at two points, the discriminant is positive, and if it does not intersect the x - axis, the discriminant is negative.

Step2: Analyze the given graph

The given graph is a parabola (since it is a quadratic graph) and it touches the x - axis at exactly one point (the vertex lies on the x - axis). This means that the quadratic equation has exactly one real root (a repeated root).

Step3: Determine the discriminant value

Since the quadratic equation has exactly one real root (a repeated root), by the property of the discriminant of a quadratic equation, the discriminant \( D = 0 \).

Answer:

0