Question

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

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).
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).
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).
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).

Answer 1

The fourth graph.

Reason: for an upward-opening parabola a positive discriminant means two real x-intercepts, which happens only if the vertex's y-value is negative. The fourth parabola has vertex (0, −1), so it crosses the x-axis twice.