1. Warm up
Factor: x2 + 6x + 9
Factor : 10x2 + 15x
Simplify
Simplify:

2. EOCT Review Is the following function even, odd, or neither? a
even b) odd c) neither

3. EOCT Review
2 b) 1/2
c) -1/2 d) -2 b

4. EOCT Review
2y b) 4xy + 2y2
c) 4xy d) 0 c

5. Lesson 2.5 - Solving Quadratic Equations in Factored Form y = x2 + 5x + 6 y = (x + 3)(x + 2)

6. Notes - Solving Quadratic Equations in Factored Form
Zero Product Property
If ab = 0, then a = 0 or b = 0
If the product of two factors is zero, then at least one of the factors must be zero.
3 * 0 = 0 0 * 3 = 0 0 * 0 = 0

7. Set each factor equal to zero and solve.
Notes - Solving Quadratic Equations in Factored Form (x + 3)(x + 2) = 0
Set each factor equal to zero and solve.
Check your answers.

8. Ex. 1: Solve the equation x2 + x – 6 = 0 (x – 2) and (x+3)
STEP 1: Factor
(x – 2) and (x+3)
STEP 2: Set each factor equal to 0.
x-2= 0 and x+3 = 0
STEP 3: Solve for x.
x-2= 0
x+3 = 0
x=-3
x = 2
STEP 4: Check your answers.
x2 + x – 6 = 0
x2 + x – 6 = 0
= 0
= 0
0 = 0
0 = 0

9. Solve (Find the x-intercepts)
2) x2 – 2x = 0
3) x2 – 8x = -12

10. (x – 5) and (x – 5) x – 5 = 0 and x – 5 = 0 x – 5 = 0 x – 5 = 0
Ex. 4: Solve the equation x2 – 10x + 25 = 0
STEP 1: Factor
(x – 5) and (x – 5)
STEP 2: Set each factor equal to 0.
x – 5 = 0 and x – 5 = 0
STEP 3: Solve for x.
x – 5 = 0
x – 5 = 0
Don’t write it twice!!!
x = 5
x = 5
STEP 4: Check your answers.
0 = 0

11. Extension (x-4) feet x feet x2 – 4x Find an expression for the area.
If the area is equal to 5 square feet, find x.
x = 5

12. We will get x squared by itself.
Then we will take the square
root of both sides of the equal sign.
There will be a positive
answer and a negative answer.

13. Let’s look at some examples where x2 is already by itself.

14. take the square root of both sides.
Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.
Here, all we have to do is
take the square root of both sides.

15. Let’s look at some examples where x2 is NOT by itself.

16. We must solve to get x2 by itself 1st!
add 48
divide by 3
take the square
root of both sides

17. We must solve to get x2 by itself 1st!
subtract 32
take the square
root of both sides

18. Falling object model
When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:

19. An engineering student is a contestant in an egg dropping
contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking. Find the time it will take for the egg to hit the ground. Disregard air resistance.
SOLUTION:
The starting height is 32 feet.
Now, substitute 0 for h and solve.
Subtract 32 from both sides
Divide both sides by –16
Take the square root of both sides
So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!! 