Chapter 9B
Table of Contents
o Day 1: SWBAT: Solve Quadratic Equations by Factoring and Graphically
Pgs: 1-6
HW: Pages 7 - 8
o Day 2: SWBAT: Solve Quadratic Word Problems by Factoring
Pgs: 9-15
HW: Pages 16-19
o Day 3: SWBAT: Solve Consecutive Integer Word Problems by Factoring
Quadratic Equations
Pgs: 20-24
HW: Pages 25-26
o Day 4: SWBAT: Solve Quadratic – Linear Systems Algebraically
Pgs: 27-30
HW: Pages 31-32
o Day 5: SWBAT: Write a quadratic equation that has given roots using
reverse factoring
Pgs: 33-37
HW: Page 38
o Day 6: SWBAT: Review Solving Equations Quadratics by using a variety
of problems
Pgs: 39-48
HW: Finish this Section
Day 1
Warm - Up: Factor Each.
1.
3.
2.
x2 - 64
x2 - 4x - 12
4. x2 - 6x
You will Learn how to Solve Quadratic Equations two ways:
Method 1: Solve by Graphing
Method 2: Solve by Factoring (Preferred Method)
1
x2 + 8x + 15 = 0
Solution: x = _____ or x = _____
Solution: x = _____ or x = _____
2
Example 3: Use the Zero Product Property
Use the Zero Product Property to solve each equation.
A. (x – 3)(x + 7) = 0
B. x(x - 5) = 0
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring.
C. x2 – 12x + 36 = 0
D. x2 + 4x = 21
3
Practice: Solve the quadratic equation by factoring.
3. x2 = -3x + 10
4. x2 + 2x = 8
Example 3: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring.
E. x2 – 5x = 0
F. x2 = -2x
Practice: Solve the quadratic equation by factoring.
5. x2 + 7x = 0
6. x2 = 11x
4
Example 4: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring.
G. x2 – 16 = 0
H. 4x2 = 25
Practice: Solve the quadratic equation by factoring.
7. x2 – 49 = 0
8. 9x2 = 100
Challenge
The graph below represents a quadratic function of the form y x2 bx c . Use the graph
to determine the zeros of the function. Then, determine the binomial factors of the function, and
express the quadratic function in its y x2 bx c form.
5
SUMMARY
Exit Ticket
1.
2.
6
Day 1 – HW
Solve each by Factoring.
1. x2 + 11x + 24 = 0
4.
x2 + 3x = 28
7.
x2
10.
= 4x + 12
x2 - 14 = 5x
x2 - 225 = 0
2.
5.
8.
3.
x2 - 3x = 0
x2 = 81
6.
x2
= 14x
25m2 = 36
9.
x2
= -10x
11. 3x2 = 48
12.
2a3 = 12a2
7
13.
x2 - 4x + 4 = 0
Solution: _________________
14. 2x2 + 4x – 6 = 0
Solution: _________________
8
Day 2 – Word Problems and Quadratic Equations
SWBAT: Solve More Quadratic Equations by Factoring
Warm – Up
1.
Quadratic Equations and Proportions
9
Section 1: Solving Quadratic Equations involving Proportions
1)
2)
3)
4)
10
Solve each Proportion.
11
12
Section 2: Solving Quadratic Equations involving Word Problems
Example 9: Solve.
The square of a number increased by twice the number is 48. Find both solutions.
Practice: Solve.
1) When 10 is subtracted from the square of a number the result is three times the
number. What is the positive solution?
13
Example 10: Solve.
The shorter side of a rectangle is 3 less than the longer side. The area is 54. Find
the length and width.
Practice: Solve.
1) The length of a rectangle is four feet longer than the width. The area is 21. Find
the dimensions.
14
Challenge Problem:
One leg of a right triangle is 1 cm longer than the other leg. The hypotenuse measures 5 cm.
Find the measure of each leg of the triangle.
Summary
Exit Ticket
1.
2.
15
Homework
Section 1: Solve each Proportion.
1)
2)
3)
16
4)
5)
6)
7)
17
Section 2: Word Problems
8) The square of a number is equal to 24 more than twice the number. Find the
negative number.
9) The square of a number is decreased by three times the number is ten. Find
the positive number.
10)
When two times a number is subtracted from the square of a number
the result is zero. Find both numbers
11)
The square of a number is decreased by five times the number is 24.
Find the number.
18
Section 3: Area Word Problems
12)
The shorter side of a rectangle is 24 less than the longer side. The area
is 81. Find the length and the width.
13)
The length of a rectangle exceeds the width by 6. The area of the
rectangle
is 27. Find the length and the width.
14)
The length of a rectangle is one more than the width. The area is 56.
Find the length and the width.
15)
The length of a rectangle is eight more than the width. The area is 9.
Find the length and the width.
19
Day 3 – Consecutive Integer Word Problems and Quadratic Equations
Solve Consecutive Integer Word Problems by Factoring
Quadratic Equations.
SWBAT:
Warm – Up:
Recall:
Consecutive Integers are integers that follow one another in order.
Ex: {5, 6, 7, 8}
{-5, -4, -3, -2}
Rule:
Consecutive Even/ODD Integers are even or odd integers that follow one another in
order.
Ex: {2, 4, 6, 8}
{-12, -10, -8, -6}
Ex: {3, 5, 7, 9}
{-5, -3, -1, 1}
Rule:
20
Example 1: The product of two consecutive positive odd integers is 1 less than four
times their sum. Find the two positive integers.
Example 6: Solve.
Find three consecutive integers such that the square of the first is equal to one more
than twice the second.
Answer: 7 and 9
Example 2: The product of two consecutive integers is 56. Find the integers
21
Practice: Solve.
The product of two consecutive even integers is 48. Find the integers
Example 3: The product of two consecutive integers is three less than three times their
sum. Find the integers.
Practice: Solve.
The product of two consecutive odd integers is 1 less than twice their sum.
Find the integers.
22
Example 4: The product of two consecutive integers is 5 more than three times the
larger. Find the integers.
Example 5:
Find three consecutive odd integers such that the product of the first and third is
one more than four times the second.
Practice: Solve.
Find three consecutive integers such that the product of the first and second is 2
more than three times the third.
23
Challenge
SUMMARY
Exit Ticket
24
Day 3 Consecutive Integer Homework
1) The product of two consecutive integers is 120. Find the integers
2) Find two consecutive even integers such that the square of the smaller is 10
more than the larger.
3) The product of two consecutive integers is six less than their sum.
Find the integers.
4)
25
5) Find three consecutive even integers such that the product of the first and
third is equal to three times the second.
6) Find three consecutive odd integers such that the square of the first
increased by twice the second is equal to two less than three times the third.
7) Find three consecutive even integers such that the product of the first and
the second is 8 more than 38 times the third.
26
Day 4
SWBAT: Solve a Quadratic - Linear System Algebraically
Warm – Up
27
Exercise 2: Solve the Quadratic Linear System below. Check your answer
y = x2 – x - 6
y = 2x - 2
Step 1: Use Substitution to replace the expressions for “each y” equal to each other.
Make sure that both equations are solved for “y” first!
__________________ = ____________
Step 2: Solve the Quadratic so that we have an equation in the form of ax2 + bx + c = 0
Step 3: Factor
Step 4: Set each factor equal to zero.
Step 5: Solve for y by plugging in the x-value into the linear equation.
x = ____
y=
x = ____
y=
Step 6: Write your answer(s) as a point.
Solutions =
28
29
CHALLENGE PROBLEM
SUMMARY
EXIT TICKET
30
HOMEWORK – Quadratic Linear Systems
1. Solve algebraically:
y = x2 - 4x + 1
y = 2x - 4
The point(s) of intersection are: ____________________
______________________________________________________________________________
2. Solve algebraically:
y = x2 - 2x + 1
y = -x + 3
The point(s) of intersection are: ____________________
31
3. Solve algebraically:
y + 3x = x2 - 10
y + 10 = -5x
The point(s) of intersection are: ____________________
______________________________________________________________________________
4. Solve algebraically:
y = -x2 + 6x - 5
y = 7 – 2x
The point(s) of intersection are: ____________________
32
Day 5
SWBAT: Write a quadratic equation that has given roots using reverse factoring
Warm – Up
Up to this point we have found the solutions to quadratics by a
factoring. Here we will take our solutions and work backwards to find
what quadratic goes with the solutions.
We will start with rational solutions. If we have rational solutions we
can use factoring in reverse, we will set each solution equal to x and
then make the equation equal to zero by adding or subtracting. Once
we have done this our expressions will become the factors of the
quadratic.
33
Example #2:
If the roots of a quadratic equation are 2 and 5, write the quadratic equation in the form
ax² +bx + c = 0.
Method 1
Method 2
Answer:
________________________________________________________________________________
Practice:
1. If the roots of a quadratic equation are -3 and 2, write the quadratic equation in the form of
ax² +bx + c = 0.
2. If the roots of a quadratic equation are -2 and 2, write the quadratic equation in the form of
ax² +bx + c = 0.
3. If the roots of a quadratic equation are 1 and -6, write the quadratic equation in the form of
ax² +bx + c = 0.
4. If the root of a quadratic equation is 6, write the quadratic equation in the form of
ax² +bx + c = 0.
34
Example #3: Write the equation of the quadratic equations below in the form of
ax² +bx + c = 0.
35
Practice: Write the equation of the quadratic equations below in the form of
ax² +bx + c = 0.
5.
6.
7.
36
Challenge
SUMMARY
Exit Ticket
1) Which factored form of a quadratic has roots of 4 and -3?
2)
37
Day 5 - Homework
Write a quadratic equation in the form of ax² +bx + c = 0 that has the given roots.
1. { -1 , -10 }
2. { 10 , -1 }
3. { 2 , -6 }
4. { 3 , -2 }
5. { -2 , -4 }
6. { 1 , -12 }
7. { -1 , -2 }
8. { 2 , -4 }
9. { 1 , -10 }
10. { -1 , -3 }
11. 5
12. { 6 , -1 }
13. { 4 , -1 }
14. { 2 , -5 }
15. { 4 , 1 }
16.
17.
18.
38
Chapter 9 Review – Quadratic Equations Review
SWBAT: Apply Their Knowledge on Solving Quadratic Equations
1. What are the solutions of (x + 4)(x – 2) = 0?
A)
B)
C)
D)
4 and -2
-4 and -2
-4 and 2
4 and 2
2. Solve x2 + 2x – 15 = 0 by factoring.
A)
B)
C)
D)
x = 5 and x = 3
x = 15 and x = 1
x = -5 and x = 3
x = -5 and x = -3
3. What are the solutions of: 0 = 2x2 – 50?
A)
B)
C)
D)
-4 and 4
-5 and 5
-2 and 2
-3 and 3
4.
39
5.
6. What is the solution set of the equation x2 – 3x = 0?
A)
B)
C)
D)
{0}
{0, 3}
{0, -3}
{3}
7. The solution set for the equation x2 + 4x = 5?
A)
B)
C)
D)
{-5, 4 }
{-4, 5}
{-5, 1}
{-1, 5}
40
8.
A) y = x2 + 7x - 10
B) y = x2 - 8x + 12
C) y = x2 - 7x + 10
D) y = x2 - 3x – 10
9.
10.
11.
41
12.
13.
14.
15.
42
16.
17.
18.
43
19.
20.
21.
44
22. Solve: x2 = 49.
23.
Solve: 25x2 + 15 = 115
24. The square of a number is equal to three less than four times a number.
Find the numbers.
45
25. Solve algebraically.
y   x2  4 x  1
y  x  3
46
26. The length of a rectangle is four feet longer than the width. The area is 21.
Find the dimensions.
27. Find three consecutive odd integers such that the square of the first increased
by twice the second is equal to two less than three times the third.
47
28.
29.
29.
48