1. Solving Quadratics

2. Factoring is fun!! USA Test Prep!!! Exceed!!!
x2 +2x - 8
x2 +2x - 8
( )( ) x x
+ 4
- 2
Factoring is fun!! USA Test Prep!!! Exceed!!!

3. Factoring is fun!! USA Test Prep!!! Exceed!!!
x2 - 5x - 14
x2 - 5x - 14
( )( ) x x
- 7
+ 2
Factoring is fun!! USA Test Prep!!! Exceed!!!

4. Factoring is fun!! USA Test Prep!!! Exceed!!!
x2 – 5x - 24
x2 – 5x - 24
( )( ) x x
+ 4
– 6
Factoring is fun!! USA Test Prep!!! Exceed!!!

5. Practice!! Use Calculator!!
Factor each
Polynomial !!!

6. Solving Quadratic Equations in Factored Form y = (x + 3)(x + 2) 0 = (x + 3)(x + 2)
Ways to solve: y = x2 + 5x + 6
x-intercepts, roots, zero’s,
solutions

7. Solve (Find the x-intercepts, roots, zeros, solutions)
1) x2 + 5x + 6 = 0
2) x2 – 2x – 8 = 0

8. For polynomials, how is factoring related to multiplying?
Factor...Solve
2x2 – 3x – 5
2x2 – 3x – 5
For polynomials, how is factoring related to multiplying?

9. Practice……….

10. Solving Quadratic Equations by taking Square Roots……

11. PRACTICE……

12. Falling Objects! Use h = -16t2 + h0
Height of the object AFTER it has fallen
TIME after the object has dropped
Object’s INITIAL height

13. Example 11
The tallest building in the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground?

14. Everything must be on the same side of the equals sign before solving
Quadratic Formula
Everything must be on the same side of the equals sign before solving

15. The Discriminant tells how many & what type of solutions the quadratic has.

16. Find the discriminant and determine the number & types of roots
Find the discriminant and determine the number & types of roots. Example: 10
2 Imaginary Roots

17. Find the discriminant and determine the number & types of roots
Find the discriminant and determine the number & types of roots. Example: 11
1 Real Root

18. Find the discriminant and determine the number & types of roots
Find the discriminant and determine the number & types of roots. Example: 12
2 Real Roots

19. Example 13 Use the quadratic formula to find the zeros.

20. Example 14: Use the quadratic formula to find the zeros.

21. Example 15: Use the quadratic formula to find the zeros.

22. Practice Problems:

23. Solving Quadratic Inequalities Algebraically

24. Answers will look like:
AND OR

25. 1. Solve and graph.

26. 2. Solve and graph.