1. Warm Up Do Objective 1b, Page 14 in the End of Course Warm Up Booklet
Factor into binomials
( )( )
Do Objective 1b,
Page 14 in the
End of Course
Warm Up
Booklet

2. Warm Up 1.) a2 + 9a + 20 2.) x2 - 9x + 18 3.) a2 - 2a - 15
Factor into binomials
( )( )
1.) a2 + 9a + 20
2.) x2 - 9x + 18
3.) a2 - 2a - 15
4.) x2 - 17x - 18
5.) 2a2 + 18a + 40

3. Warm Up
1.) a2 + 9a + 20
(a + 4)(a + 5)
2.) x2 - 9x + 18
(x - 3)(x - 6)

4. Warm Up
3.) a2 - 2a - 15
(a + 3)(a - 5)
4.) x2 - 17x - 18
(x + 1)(x - 18)

5. Warm Up
5.) 2a2 + 18a + 40
2(a2 + 9a + 20)
2(a + 4)(a + 5)

6. Can you think of 2 #’s that you can put in the boxes that solve the following equation without using 0. = .

7. Zero-Product Property
If xy = 0, then what must x and y or both equal?
x or y must be 0.

8. Zero-Product Property
If the product of two values is zero, then one or both of the values must be zero.

9. Zero-Product Property
If x(x + 1) = 0, then what do x and (x + 1) or both equal?
Then let x = 0 and x + 1 =0
So.. x = 0 or x = 0 -1
x = -1

10. Zero-Product Property
If (2a - 1)(a + 3) = 0, then
Let 2a - 1 = 0 & a + 3 = 0
S0… 2a - 1 = 0 a + 3 = 0
2a = a = -3
a = 1/2

11. Zero-Product Property
To solve a quadratic equation, simply set both binomials equal to 0….
Your Turn
Solve (x + 3)(x+ 4) = 0

12. Zero-Product Property
Solve (x + 3)(x+ 4) = 0
x + 3 = 0 & x + 4 = 0
x = x = -4

13. (Solve)
1.) x2 + 6x - 7 = 0
In order to solve a quadratic equation:
1.) First factor
2.) Then set each ( ) = 0

14. Set both (x - 1) and (x + 7) equal to ZERO.
(Solve)
1.) x2 + 6x - 7 = 0
(x- 1)(x +7) = 0
Set both (x - 1) and (x + 7) equal to ZERO.
x - 1 = 0 & x + 7 = 0
x = & x = -7

15. (1)2 + 6(1) - 7 = 0 1 + 6 - 7 = 0 0 = 0 Check 1.) x2 + 6x - 7 = 0
x = 1 and x = -7
(1)2 + 6(1) - 7 = 0
= 0
0 = 0
True

16. (-7)2 + 6(-7) - 7 = 0 49 - 42 - 7 = 0 0 = 0 Check 1.) x2 + 6x - 7 = 0
x = 1 and x = -7
(-7)2 + 6(-7) - 7 = 0
= 0
0 = 0
True

17. Set both (x ) and (x - 3) equal to ZERO.
(Solve)
2.) x2 - 3x = 0
x(x - 3) = 0
Set both (x ) and (x - 3) equal to ZERO.
x = 0 & x - 3 = 0
& x = 3

18. Solving Quadratics
What are the 2 steps required to solve a quadratic equation……
1.) Factor
2.) Solve

19. Set both (x + 1) and (x + 5) equal to ZERO.
Practice (Solve)
Your Turn
3.) x2 + 6x + 5 = 0
(x + 1)(x + 5) = 0
Set both (x + 1) and (x + 5) equal to ZERO.
x + 1 = 0 & x + 5 = 0
x = & x = -5

20. (Solve )
1.) x2 + 4x - 5 = 0
2.) x2 + x - 6 = 0
3.) x2 - 2x - 3 = 0
4.) x2 - 3x - 10 = 0

21. Try These (Solve)
1.) x2 + 6x - 7 = 0
2.) x2 + x - 12 = 0
3.) x2 + 6x + 5 = 0
4.) x2 - 4x - 12 = 0