1. Solve using factoring or square root property.
Warm-up
Solve using factoring or square root property.
𝑚 2 −6𝑚−16=0
6 𝑥 2 −5𝑥=4
𝑚 2 −49=0
2 𝑝 2 −18=0

2. It’s called finding the discriminant.
There is a way to tell how many roots an equation will have.
4.8
It’s called finding the discriminant.
The discriminant is a small part of the quadratic formula.

3. Window (Foldable) Notes
Fold your paper over (top to bottom leaving about an inch at the bottom).
Positive
Zero
Negative
Discriminant

4. Note: Solutions and roots are the same.
If the answer is POSITIVE, then you will have 2 real roots.
If the answer is ZERO, then you will have 1 real root.
If the answer is NEGATIVE, then you will have no real roots.
Note: Solutions and roots are the same.

5. Determine the number of roots. Example: 1
No Roots

6. Determine the number of roots. Example: 2

7. Determine the number of roots. Example: 3

8. How does the discriminant relate to the graph of a quadratic function?

9. Find the number of x-intercepts. Example: 4
2 ROOTS

10. Find the number of x-intercepts. Example: 5
No x-intercepts
No ROOTS

11. Critical Thinking – With a Partner
Why is it not possible for a quadratic equation to have more than two solutions?
Determine the value(s) of k for which
No real solution
One real solution
Two real solutions