1. Entry Task
Factor
9x2 – 25
(3x – 5)(3x + 5)

2. Homework x = -3 x = 3/2 (-3,-7) (3/2, 31/4) (0,11) (0,10) Minimum
Shift left 3 down 7, stretch by a factor of 2
x = 3/2
(3/2, 31/4)
(0,10)
Minimum
(3/2, 31/3)
y = (x-3/2)2 +31/4
3(5x-3)(5x+3)
(x+5) (x-9)
(x+6) (x-4)
2(x-3) (x+5)
(3x+1) (x-5)
(2x-5) (2x+1)

3. 4.5 Solving Quadratic Equations by Factoring
Learning Target: I can solve equations by factoring
Success Criteria: I can find the zeros of a given equation

4. Think about it…. If AB = 0 what do you know must be true?
Write down what you think

5. Let’s think about this…. Number your notes 1-5
What is x in each of these questions?
1) 4x = 0
2) 4 (x+1) = 0
3) (4 + 1) (x+1) = 0
4) (x + 2) (x + 3) = 0
5) Write a sentence that explains what you just did and how you knew the answer.

6. For any real numbers a and b, if ab=0, then either a=0, b=0, or both.
Zero Product Property
For any real numbers a and b, if ab=0, then either a=0, b=0, or both.

7. The solutions are -3 and 1/2.
In this first example, the equation is already factored and is set equal to zero. To solve, simply set the individual factors equal to zero.
The solutions are -3 and 1/2.

8. Let’s look at this one…. What’s step 1?
In this example, you must set the equation equal to zero before factoring. Then set the individual factors equal to zero and solve.

9. Now, try several problems
Now, try several problems. Write these on your own paper, showing all steps carefully.
Shortly you will become the teacher…
First, Choose 3 of these problems and do them in your notes showing ALL steps
Second, we will trade with our partner and they will grade it
A = Perfect job!
B = Simple math mistake
C = multiple simple mistakes
D = had some trouble following their work or some concept mistakes
F = Didn’t try it
1) (3y-5)(2y+7)
2) x2 + x = 12
3) x2 + 2x – 15 = 0
4) - x2 = 6x + 8
5) 18x2 – 1 = 3u
6) 2x = -16x
After completion,
click here.

10. Here are the answers. For help, click on the numbers.1. 2.
3. x = -5 or x = 3
4. x = -4 or x = -2 5.
6. x = -6 or x = -2 If all are correct, you’re finished!
Click to the last slide for homework

11. #1
Back to questions

12. #2
Back to questions

13. #3 0 = x2 + 2x – 15 x2 + 2x – 15 = 0 (x+5)(x-3) – 0
x+5 = 0 or x – 3 = 0
x = -5 or x = 3
Back to questions

14. #4 -x2 = 6x + 8 x2 +6x + 8 = 0 (x+4)(x+2) = 0 (x+4) = 0 or (x+2) = 0
Back to questions

15. #5
Back to questions

16. #6 2x2 + 24 = -16x 2x2 +16x + 24 = 0 (2x+12)(x+2) = 0
(2x+12) = 0 or (x+2) = 0
2x = -12 or x = -2
x = -6 or x = -2
Back to questions

17. Homework
p odds and 36, 38 and 40
– Due Wednesday

18. Factor using “difference of two squares.”
In this example, you must first factor the equation. Notice the familiar pattern. After factoring, set the individual factors equal to zero.
Factor using “difference of two squares.”

19. This one uses a different technique than the previous ones
This one uses a different technique than the previous ones. Really, this is something you should consider at the beginning of every factoring problem. See if you can solve it.
Did you take out GCF?

20. Re-write this example in the proper form
Re-write this example in the proper form. Notice that the leading coefficient is not one. Use an appropriate factoring technique. Then solve as you have done before.

21. #3
Back to questions

22. #4
Back to questions