1. Warm-Up: September 30 / October 1, 2015 Factor each expression
2x2 + 7x – 4
4x2 – 13x + 3
9x2 + 9x + 2

2. Homework Questions?

3. Quadratic Equations
Section P.8

4. Essential Question
How can we solve quadratic equations?

5. Quadratic Equations A quadratic is a second-degree polynomial
The general form is

6. Zero Product Property If AB = 0, then A = 0 or B = 0
Use to solve a quadratic
Write the quadratic in general form
Factor the quadratic
Set each factor equal to zero
Solve each equation

7. You-Try #1: Solve by Factoring

8. Solving Quadratics Using Square Roots
Use when you have x2 + c = 0 (b=0)
Also used when you have an expression squared and a number (u2=d)
Get the squared term by itself
Take the square root of both sides
Remember ±

9. You-Try #2: Solve with Square Root

10. Completing the Square
Given 𝑥 2 +𝑏𝑥, we can create a perfect square trinomial by dividing b by 2, squaring it, and adding it
When solving, you must have one side be “ 𝑥 2 +𝑏𝑥”
Remember that whatever you add to one side, you must add to the other side

11. Example 3: Completing the Square (#27-37)
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial

12. You-Try #3: Completing the Square (#27-37)
Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial

13. Example 4a: Solving by Completing the Square

14. You-Try #4: Solving by Completing the Square

15. Example 4b: Solving by Completing the Square

16. The Quadratic Formula

17. You-Try #5: Solving using Quadratic Formula

18. The Discriminant: b2 – 4ac
The value of the discriminant tells you the number and type of solutions you will have
Discriminant
Solutions to ax2 + bx + c = 0
b2 – 4ac < 0
b2 – 4ac = 0
b2 – 4ac > 0
Is a perfect square
Not a perfect square

19. The Discriminant: b2 – 4ac
The value of the discriminant tells you the number and type of solutions you will have
Discriminant
Solutions to ax2 + bx + c = 0
b2 – 4ac < 0
No real solutions
b2 – 4ac = 0
One real solution
b2 – 4ac > 0
Is a perfect square
Two rational solutions
Not a perfect square
Two irrational solutions

20. Example 6: Using the Discriminant (#63-69)
Compute the discriminant. What does the discriminant indicate about the number and type of solutions?

21. You-Try #6: Using the Discriminant (#63-69)
Compute the discriminant. What does the discriminant indicate about the number and type of solutions?

22. What method should I use?
If 𝑎 𝑥 2 +𝑏𝑥+𝑐 can easily be factored, then factor and use zero product property.
If 𝑏=0, use square root method
If you have something in parentheses squared, use square root method.
If 𝑎 𝑥 2 +𝑏𝑥+𝑐 cannot be factored, use quadratic formula
See page 94 if you need more help choosing what method to use.

23. Assignment
Read Section P.8
Page 97 #1-93 Every Other Odd, 99, 119