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Question 7 • CMS 2026-2027 NC Math 2 CREDIT RECOVERY

Which is the graph of a quadratic equation that has a positive discriminant?

Answer

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 1, 0), and goes through (1, 4).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 2, 5), has a vertex at (0, 1), and goes through (2, 5).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex at (1, 0), and goes through (3, 4).

Image with description On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (0, negative 1), and goes through (2, 3).

Explanation

A quadratic has a positive discriminant when it has two distinct real roots, which appear as two x-intercepts. In choice D, the parabola opens upward and its vertex is at (0, −1), below the x-axis, so it crosses the x-axis twice. Using the point (2, 3), its equation is y = x² − 1, whose discriminant is 0² − 4(1)(−1) = 4, which is positive.

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