1. Bell Ringer (in your Math Journal)
1. What are the 3 forms of the
graphs of quadratics?
2. What are the 4 names for the
answers of a quadratic equation?
3. What must a quadratic equation
be equal to before you can factor it?

2. The Discriminant, the Quadratic Formula, and Completing the Square
Thursday October 1, 2015

3. Standard Form of a Quadratic Equation

5. The Discriminant

6. The Discriminant The Discriminant is: Way to solve:
Number and kind of solutions
Positive and Square
Factor
2 Rational
Zero
1 Rational
Positive not square
Quadratic formula or Complete the square
2 Irrational
Negative
2 Imaginary Solutions

7. Picture: Positive Discriminant
2 Real Solutions

8. Picture: Zero Discriminant
1 Real Solution
“Double root”

9. Picture: Negative Discriminant
0 Real Solution. 2 Complex Solutions.

10. Using the discriminant

11. Using the discriminant

12. Now we can find the square root of a negative!

13. Using the discriminant

14. Using the discriminant

15. Steps for Completing the Square
1) Write the quadratic in Standard Form
2) Divide all terms by “a”
3) Move the constant to the right side of the equation
4) Add (b/2)2 to both sides of the equation to make the left a perfect square trinomial
5) Write the left in factored form
6) Take the square root of both sides
7) Subtract the constant from both sides to get x =

16. Ex:
2x2 – 4x = 6
Step 1) 2x2 – 4x – 6 = 0
Step 2) x2 – 2x – 3 = 0
Step 3) x2 – 2x = 3
Step 4) x2 – 2x + 1 = 3 + 1
Step 5) (x – 1)2 = 4
Step 6) x – 1 = +/- 2
Step 7) x = 3, -1

17. Classwork:
Solving Quadratics in Various Ways Some with Complex Solutions
Discriminant (1-4), Quadratic Formula (1-4), Completing the Square (1-4)
Homework: Discriminant and Solving Quadratics Using Any Method