1. 13.4 The Quadratic Formula and Discriminant

2. Quadratic Formula
The boy with the negative attitude couldn’t decide whether to go to the radical party or b² and miss out on the 4 awesome chicks the party is over at 2am

3. Quadratic Song to Pop Goes the Weasel
x equals negative b
Plus or minus the square root
Of b squared minus four a c
All over 2a

4. Video Time

5. Example 1:3x2 – 9x + 1 = 0

6. Ex 2: 2x2 = 4 – 7x
2x2 + 7x – 4 = 0

7. Ex 3: Solve: 3x2 – 4x - 2 = 0

8. Ex :4 Solve: x2 - 4x - 7 = 0

9. Special Case: 3-x(x-3)=4 Need to put it in standard form
Then put it in the quadratic equation
a= 1, b=-3, c=1

10. b² - 4ac = discriminant Discriminant
Determines the number of real-number solutions of a quadratic equation
b² - 4ac = discriminant

11. Discriminant of a Quadratic 3 possibilities
b²-4ac
1.) If positive then 2 solutions for x
2.) If 0 then 1 solution for x
3.) If negative then no real solutions for x

12. Ex 5: How many solutions? 3x2 – 5x + 1 = 0
“discriminate”
Negative: no solution
Zero: one solution
Positive: two solutions
2 solutions

13. Ex 6: How many solutions? y = x2 – 3x + 7 = 0
“discriminate”
Negative: no solution
Zero: one solution
Positive: two solutions
0 solutions

14. Ex: 7How many solutions? f(x) = x2 – 12x + 36 = 0
“discriminate”
Negative: no solution
Zero: one solution
Positive: two solutions
1 solutions

15. Assignment: Page 593 # 2-28, 42-62 finding the roots is the same as solving for x