Discover the relationship between the value of the discriminant and the nature of the roots of quadratic functions.

• Students will determine the relationship between the value of the discriminant and the nature of the roots of a quadratic function.
• Students will use the value of the discriminant to identify the number of roots of a quadratic function.
• Students will identify whether, based on the value of the discriminant, the graph of a quadratic function intersects the x-axis in zero, one, or two points.
• Students will determine the nature of the roots based upon the graph of a quadratic function.

• discriminant
• quadratic formula
• parameters
• nature of the roots

This lesson involves discovering the relationship between the value of the discriminant and the nature of the roots of quadratic functions. As a result, students will:

• Use a slider to generate graphs of random quadratic functions.
• Make conclusions about the relationship between the value of the discriminant and the nature of the roots for the three cases.