Question

question 6 of 10
using the graph as your guide, complete the following statement.
the discriminant of the function is ____.

a. negative
b. positive
c. zero

Explanation:

The graph of the quadratic function is a parabola that touches the x - axis at exactly one point (it has a single vertex on the x - axis). For a quadratic function \(y = ax^{2}+bx + c\), the discriminant is given by \(D=b^{2}-4ac\). When the parabola touches the x - axis at one point, it means the quadratic equation \(ax^{2}+bx + c = 0\) has exactly one real root (a repeated root). The discriminant is zero when there is exactly one real root (or a repeated real root) for the quadratic equation. If the discriminant was positive, the parabola would intersect the x - axis at two distinct points, and if it was negative, the parabola would not intersect the x - axis at all. Since the given parabola touches the x - axis at one point, the discriminant is zero.

Answer:

C. zero