1. The Discriminant
CA 22.0, 23.0

2. Objective - To use the discriminant to determine the number of real solutions for a quadratic.

3. The “Parts” of the Quadratic Formula
The DISCRIMINANT
The axis of symmetry

4. Quadratic Formula
Discriminant
Used to find the
number of roots
(how many roots).
Used to find the
roots of a quadratic
equation...
Two real
roots
One real
root
No real
roots

5. Determine the number of roots for the quadratic
equation below.
Two Real Solutions

6. Determine the number of x-intercepts for the
quadratic equation below.
No Real Solution

7. Determine the number of x-intercepts for the
quadratic equation below.
One Real Solution

8. b c a Match each equation below with its graph. a) b) c) No Real Roots
Two Real Roots a
One Real
Root

9. Tell whether the vertex lies above, below, or on
the x-axis.
Opens up
Opens down
No Real Roots
Two Real Roots
Vertex lies
Above x-axis
Vertex lies
Above x-axis