1. Solving Quadratic Equations Quadratic Formula Medina (Revised 2/26/14 ep)1

2. Quadratic Formula Song https://www.youtube.com/watch?v=2lbABbfU6Zc

3. Solving Quadratic Equations by using the Quadratic Formula Any quadratic equation can be solved using the Quadratic Formula we just have to remember to

4. Analyzing the Discriminant Discriminant It is this part of the quadratic formula that will enable you to DETERMINE the…. Positive Value in the discriminant: ZERO: Negative Value: number of solution(s) a quadratic equation has. Means there are 2 solution(s). Means there are 1 solution. Means there is no real solution ★ If discriminant is a perfect square, the quadratic is factorable and if the discriminant is not a perfect square, it is best to use quadratic formula to find the 2 solutions

5. Discriminant vs. Quadratic Formula https://www.youtube.com/watch?v=2lbABbfU6Zc

6. Discriminant vs. Quadratic Formula Example 1: 7 1 12 The discriminant is a positive value so we know this quadratic has two solutions and 1 is a perfect square therefore this quadratic can also be solved by factoring too. How many solution does the quadratic function have? What are the solution(s) to the quadratic function? 7 1 What we don’t know is what the values of those solutions are!

7. Discriminant vs. Quadratic Formula Example 2: 8 1 16 The discriminant is zero so we know this quadratic has only 1 solution and 0 is a perfect square therefore this quadratic can also be solved by factoring too. How many solution does the quadratic function have? What are the solution(s) to the quadratic function? 8 1 ★ Since the square root of zero is just zero, it can not be positive or negative. We evaluate like the ± isn’t there. What we don’t know is what the value of this solution is!

8. Discriminant vs. Quadratic Formula Example 3: -2 2 3 The discriminant is a negative value so we know this quadratic has no real solution. therefore this quadratic could not be solved by factoring. How many solution does the quadratic function have? What are the solution(s) to the quadratic function? 7 1 It is unnecessary to continue with the quadratic formula because we already know there is no real solution!

9. Discriminant vs. Quadratic Formula Example 4: -4 11 The discriminant is a positive value so we know this quadratic has two solutions and 12 is NOT a perfect square therefore this quadratic can not be solved by factoring. How many solution does the quadratic function have? What are the solution(s) to the quadratic function? -4 1 Simplify the radical What we don’t know is what the values of those solutions are! Since the solution has a radical we don’t have to split up BUT we do have to reduce if possible. Does 2 divide evenly into each the constant and coefficient??? YES!!!

10. Discriminant vs. Quadratic Formula Example 5: 5 1 6 The discriminant is a positive value so we know this quadratic has two solutions and 1 is a perfect square therefore this quadratic can also be solved by factoring too. How many solution does the quadratic function have? What are the solution(s) to the quadratic function? 5 1 What we don’t know is what the values of those solutions are!

11. Discriminant vs. Quadratic Formula Example 6: 0 4 -36 How many solution does the quadratic function have? What are the solution(s) to the quadratic function? 0 4

12. Quadratic Formula Song https://www.youtube.com/watch?v=cYpPa3Jt3-I