Introduction to the Quadratic Formula — Quiz

Question 4 • Algebra I

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

Answer

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. An upward-opening parabola has a vertex at the point negative 1 comma 0. It passes through approximately the points negative 2 comma 1 and 0 comma 1, then continues upward through approximately negative 3 comma 4 and 1 comma 4.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. An upward-opening parabola has a vertex at the point 0 comma negative 1. It passes through approximately the points negative 1 comma 0 and 1 comma 0, then continues upward through approximately negative 2 comma 3 and 2 comma 3.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. An upward-opening parabola has a vertex at the point 1 comma 0. It passes through approximately the points 0 comma 1 and 2 comma 1, then continues upward through approximately negative 1 comma 4 and 3 comma 4.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. An upward-opening parabola has a vertex at the point 0 comma 1. It passes through approximately the points negative 1 comma 2 and 1 comma 2, then continues upward through approximately negative 2 comma 5 and 2 comma 5.

Explanation

A quadratic has a positive discriminant when its graph crosses the x-axis at two distinct points, since those crossings are two distinct real roots. Choice B has a vertex at (0, −1) and crosses the x-axis at (−1, 0) and (1, 0), so it has two distinct roots. Choices A and C touch the x-axis only at their vertices, and D does not meet the x-axis.

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