1. Unit 1B quadratics
Day 6

2. Quadratic Formula and Discriminant
EQ: How do we use the Quadratic Formula and tell how many solutions a function has?
M2 Unit 1B: Day 6

3. Quadratic Formula

4. Remember The equation must = 0 before using the QF
You must label a, b, and c

5. Use the QF to solve:

6. Use the QF to solve:

7. Use the QF to solve:

8. Use the QF to solve:

9. Use the QF to solve:

10. Use the QF to solve:

11. Let’s look at the different solutions that we got
In we got
In we got
In we got
The expression under the radical (the radicand) determines what the solution will look like.
We call the radicand in the QF
the DISCRIMINANT

12. Let’s explore and compare the discriminants
In we got
In we got
In we got

13. The Discriminant: tells us how many and what type of solutions we will get
Positive
2 real solutions
zero
1 real solutions
Negative
2 imaginary solutions

14. Find the discriminant to determine how many solutions and what type they are. Draw a quick sketch.
2 imaginary solutions
2 real solutions
Opens up, does not cross x-axis.
Opens down, crosses x-axis twice.

15. Find the discriminant to determine how many solutions and what type they are. Draw a quick sketch.
2 real solutions
1 real solution
Opens up, crosses x-axis twice.
Opens up, crosses x-axis once.

16. Homework:
Textbook: Pg. 93 # 1 – 11