Question

question 10 of 10
using the graph as your guide, complete the following statement.
the discriminant of the function is ____.
graph of a parabola opening upwards, not touching or crossing the x - axis
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a. positive
b. zero
c. negative

Explanation:

Step1: Recall discriminant - graph relation

For a quadratic function \( y = ax^2 + bx + c \), the discriminant \( D = b^2 - 4ac \) relates to the x - intercepts:

• If \( D>0 \), the parabola has two distinct x - intercepts.
• If \( D = 0 \), the parabola has one x - intercept (vertex on x - axis).
• If \( D<0 \), the parabola has no x - intercepts.

Step2: Analyze the given graph

The graph of the quadratic function (parabola) intersects the x - axis at two distinct points (since it crosses the x - axis twice). This means the quadratic equation \( ax^2+bx + c = 0 \) has two distinct real roots. By the discriminant - root relationship, when there are two distinct real roots, the discriminant \( D=b^2 - 4ac>0 \), i.e., the discriminant is positive.

Answer:

A. positive