1. Do Now: Draw the picture. THINK what do you want to find?
Ch. 4.4 Factor Quadratic Equation How can I find common binomial factors of quadratic expression with lead coefficient of 1
Do Now: Draw the picture. THINK what do you want to find?
On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of the bridge is in the shape of the parabola
f(x) = 0.1x2  7x + 250, where f(x) is the height in feet of the cable above the roadway at the distance x feet from a support tower.
a. What is the closest the cable comes to the roadway?
b. How far from the support tower does this occur?
Success Criteria:
Today’s Agenda
Factor ax2 + bx + c when a is ±1
Find common Factors
Do Now
Investigate: Factoring Quadratics
Assignment

2. Announcements

3. What do you know? (x - 4)(x +5) FOIL Combine like terms Constant
Distribute
Coefficient
Multiply variables
Factors
Binomials
Product
Quadratic
Variable
Parabola
Trinomial
Write the problem on a public record and write words that relate to the problem.

4. Coefficient of Middle Term
Let’s Investigate How can I find common binomial factors of quadratic expression with lead coefficient of 1
A. BEFORE Multiplying the binomials, CIRCLE the constant term in the parentheses. These will be constant 1 and constant 2 in the table.
1) (x + 2)(x + 4) =
2) (x + 5)(x + 6) =
3) (x - 1)(x + 6) =
4) (x + 1)(x + 3) =
5) (x + 4)(x - 2) =
6) (x - 3)(x - 3) =
B. Fill in the first 2 columns of the table with the numbers you circled.
Number
Binomial
factors
Constant 1
Constant 2
Coefficient of Middle Term
Constant 3
Simplified Product (trinomial) #1
(x + 2)(x + 4) #2
(x + 5)(x + 6) #3
(x - 1)(x + 6) #4
(x + 1)(x + 3) #5
(x + 4)(x - 2) #6
(x - 3)(x - 3)

5. Coefficient of Middle Term
Let’s Investigate
C. Find the product of each of the expressions from part A.
Foil
Distribute
Simplify
1) (x + 2)(x + 4) =
2) (x + 5)(x + 6) =
3) (x - 1)(x + 6) =
4) (x + 1)(x + 3) =
5) (x + 4)(x - 2) =
6) (x - 3)(x - 3) =
Using the product in part C, UNDERLINE the coefficient of the middle term and box the constant term, which will be constant 3 in the table.
Complete the table using the information from part C.
Number
Binomial
Factors
Constant 1
Constant 2
Coefficient of Middle Term
Constant 3
Simplified Product (trinomial) #1
(x + 2)(x + 4) 2   4 6  8 
 x2 + 6x + 8 #2
(x + 5)(x + 6)  5  6
 11
 30
x2 + 11x + 30 #3
(x - 1)(x + 6)
 -1
 -6
 x2 + 5x - 6 #4
(x + 1)(x + 3)  1  3
 x2 + 4x + 3 #5
(x + 4)(x - 2)
 -2  2
 -8
x2 + 2x – 8 #6
(x - 3)(x - 3)
 -3  9
x2 - 6x + 9

6. Do Now: Draw the picture. THINK what do you want to find?
Ch. 4.4 Factor Quadratic Equation How can I find common binomial factors of quadratic expression with lead coefficient of 1
Do Now: Draw the picture. THINK what do you want to find?
Fireworks are fired from the roof of a 100-foot building and travel 84 feet per second.
The equation h(t) = -16t2 + 84t models the height h of the fireworks at any given time t seconds.
How long are the fireworks in the air?
How high were the fireworks after 2 seconds?
Success Criteria:
Today’s Agenda
Factor ax2 + bx + c when a is ±1
Find common Factors
Do Now
Investigate: Factoring Quadratics
Assignment

7. Generalize
Use the information from the table to answer the questions: (Be ready to Discuss and Share)
What do you notice about the coefficient of the linear term in relation to constant 1 and constant 2? What do you notice about the signs?
What do you notice about the constant 3 in relation to constant 1 and constant 2? What do you notice about the signs?
Using the information, how can we undo distributing? How can we factor a trinomial to 2 binomials?
On the Back of your paper lets factor: x2 + 10x2 – 24

8. Factoring Trinomials x + bx + c Positive b and c2
Factoring Trinomials x + bx + c Positive b and c
Ex x x + 24
( )( )
Trinomials can factor into
2 binomials.
When the lead coefficient is 1,
the first terms are the square
root of the variable.
x x
1. The signs are determined by
term c. If c is positive the signs
are the same.
2. Then look at the sign of the b
term, if it is (-) they are
both (-). If it is (+) then both
signs are (+).

9. Factoring Trinomials x + bx + c Positive b and c2
Factoring Trinomials x + bx + c Positive b and c
Ex x x + 24
( )( )
3. Determine the factors of c. 24
x x
4. Because the signs are the
same we add the factors
together to find the middle
value. These are the factors
of the trinomial

10. Factoring Trinomials x - bx + c negative b and positive c2
Factoring Trinomials x - bx + c negative b and positive c
Ex x x + 22
( )( )
1. Look at sign for c.
(positive means same sign)
x x
2. Look at the sign for b (-).
Then they are both (-).
3. Factor c
4. What factors are the
sum of b?

11. Factoring Trinomials x2 - bx - c with negative c
Ex x2 - 8x – 20
( )( )
1. Look at sign for c.
(negative means opposite signs)
x x
2. Find the factors of c. 20
3. Since signs are opposite
you must subtract factors
to find the middle term. Keep
the signs with the terms.

12. Practice HW #27 A. x2 - 5x + 4 F. x2 - 5x - 36 B. x2 + 15x + 36
C. x2 - 18x + 45
D. x2 - 7x + 12
E. x2 - 5x - 14
F. x2 - 5x - 36
G. x2 + 18x - 40
x2 + 10x – 24
x2 + 10x + 24
J. x2 + 9x – 13