SWBAT: Solve Consecutive Integer Word Problems by
Factoring Quadratic Equations
B
D
-40
-5
8
3
𝑥 +3
𝑥= 𝟓
𝒙(𝒙 + 𝟑) = 𝟒𝟎
𝒙𝟐 +𝟑𝒙 = 𝟒𝟎
𝒙𝟐 + 𝟑𝒙 − 𝟒𝟎 = 0
𝒙+𝟖 𝒙−𝟓 =𝟎
𝒙+𝟖 =𝟎
𝒙 = −𝟖
Reject
𝒙−𝟓 =𝟎
𝒙=𝟓
SWBAT: Solve Consecutive Integer Word Problems by
Factoring Quadratic Equations
Homework
SWBAT:
Equations
Solve Consecutive Integer Word Problems by Factoring Quadratic
SWBAT:
Equations
Solve Consecutive Integer Word Problems by Factoring Quadratic
SWBAT:
Equations
Solve Consecutive Integer Word Problems by Factoring Quadratic
First x
Second x + 1
-56
-7
8
1
𝑭𝒊𝒓𝒔𝒕 × 𝑺𝒆𝒄𝒐𝒏𝒅 = 𝟓𝟔
𝒙(𝒙 + 𝟏) = 𝟓𝟔
𝒙𝟐 +𝟏𝒙 = 𝟓𝟔
𝒙𝟐 + 𝟏𝒙 − 𝟓𝟔 = 0
𝒙+𝟖 𝒙−𝟕 =𝟎
𝒙+𝟖 =𝟎 𝒙−𝟕 =𝟎
𝒙 = −𝟖
𝒙=𝟕
x = -8
x=7
First
Second x + 1 = -7 x + 1 = 8
SWBAT:
Equations
Solve Consecutive Integer Word Problems by Factoring Quadratic
First x
Second x + 2
-48
-6
8
2
𝑭𝒊𝒓𝒔𝒕 × 𝑺𝒆𝒄𝒐𝒏𝒅 = 𝟒𝟖
𝒙(𝒙 + 𝟐) = 𝟒𝟖
𝒙𝟐 +𝟐𝒙 = 𝟒𝟖
𝒙𝟐 + 𝟐𝒙 − 𝟒𝟖 = 0
𝒙+𝟖 𝒙−𝟔 =𝟎
𝒙+𝟖 =𝟎 𝒙−𝟔 =𝟎
𝒙 = −𝟖
𝒙=𝟔
x = -8
x=6
First
Second x + 2 = -6 x + 2 = 8
SWBAT:
Equations
Solve Consecutive Integer Word Problems by Factoring Quadratic
First x
Second x + 1
F
S
x=0
x=5
x+1=1
x+1=6
𝒙=𝟎
𝑭 ∙ 𝑺 = 𝟑 𝒔𝒖𝒎 − 𝟑
𝒙(𝒙 + 𝟏) = 𝟑(𝟐𝒙 + 𝟏) − 𝟑
𝒙𝟐 + 𝟏𝒙 = 𝟔𝒙 + 𝟑 − 𝟑
𝒙𝟐 + 𝟏𝒙 = 𝟔𝒙
−𝟔𝒙 = −𝟔𝒙
0
𝒙𝟐 − 𝟓𝒙 = 𝟎
-5
0
𝒙 𝒙−𝟓 =𝟎
-5
𝒙−𝟓 =𝟎
𝒙=𝟓
SWBAT: Write a Quadratic Equation and Solve.
First x
Second x + 2
F
S
x = -1
x=3
x+2=1 x+2=5
𝑭 ∙ 𝑺 = 𝟐 𝒔𝒖𝒎 − 𝟏
𝒙(𝒙 + 𝟐) = 𝟐(𝟐𝒙 + 𝟐) − 𝟏
𝒙𝟐 +𝟐𝒙 = 𝟒𝒙 + 𝟒 − 𝟏
𝒙𝟐 +𝟐𝒙 = 𝟒𝒙 + 𝟑
−𝟒𝒙 − 𝟑 = −𝟒𝒙 -3
𝒙𝟐 −𝟐𝒙 − 𝟑 = 𝟎
𝒙+𝟏 𝒙−𝟑 =𝟎
𝒙+𝟏 =𝟎 𝒙−𝟑 =𝟎
𝒙 = −𝟏
𝒙=𝟑
-3
-3
1
-2
SWBAT: Write a Quadratic Equation and Solve.
First x
Second x + 1
x=4
F x = -2
S x + 1 = -1 x + 1 = 5
𝑭 ∙ 𝑺 = 𝟑 𝑺𝒆𝒄𝒐𝒏𝒅 + 𝟓
𝒙 𝒙+𝟏 =𝟑 𝒙 +𝟏 +𝟓
𝒙𝟐 + 𝟏𝒙 = 𝟑𝒙 + 𝟑 + 𝟓
𝒙𝟐 +𝟏𝒙 = 𝟑𝒙 + 𝟖
−𝟑𝒙 − 𝟖 = −𝟑𝒙 − 𝟖
𝒙𝟐 −𝟐𝒙 − 𝟖 = 𝟎
𝒙+𝟐 𝒙−𝟒 =𝟎
𝒙+𝟐 =𝟎 𝒙−𝟒 =𝟎
𝒙 = −𝟐
𝒙=𝟒
-8
2 -4
-2
SWBAT: Write a Quadratic Equation and Solve.
Example 5:
Find three consecutive odd integers such that the product of
the first and third is one more than four times the second.
𝐹𝑖𝑟𝑠𝑡
𝑥
𝑆𝑒𝑐𝑜𝑛𝑑
Third
𝑥 + 2
𝑥 + 4
F
S
T
x = -3
x=3
x + 2 = -1
x+2=5
x+4= 1
x+4=7
𝑭 ∙ 𝑻 = 𝟒 𝑺𝒆𝒄𝒐𝒏𝒅 + 𝟏
𝒙 𝒙+𝟒 =𝟒 𝒙 +𝟐 +𝟏
𝒙𝟐 +𝟒𝒙 = 𝟒𝒙 + 𝟖 + 𝟏
𝒙𝟐 +𝟒𝒙 = 𝟒𝒙 + 𝟗
−𝟒𝒙 − 𝟗 = −𝟒𝒙 −𝟗
𝒙𝟐 −𝟗 = 𝟎
𝒙+𝟑 𝒙−𝟑 =𝟎
𝒙+𝟑 =𝟎 𝒙−𝟑 =𝟎
𝒙 = −𝟑
𝒙=𝟑
𝒙𝟐 −
𝟗 = 𝟎
SWBAT: Write a Quadratic Equation and Solve.
Practice: Solve.
Find three consecutive integers such that the product of the
first and second is 2 more than three times the third.
𝐹𝑖𝑟𝑠𝑡
𝑆𝑒𝑐𝑜𝑛𝑑
Third
F
x = -2
S
x + 1 = -1
T
x+2= 0
𝑭 ∙ 𝑺 = 𝟑 𝑻𝒉𝒊𝒓𝒅 + 𝟐
𝒙 𝒙+𝟏 =𝟑 𝒙 +𝟐 +𝟐
𝑥 +1
𝟐
𝒙
+ 𝟏𝒙 = 𝟑𝒙 + 𝟔 + 𝟐
𝑥 +2
𝟐
𝒙
+𝟏𝒙 = 𝟑𝒙 + 𝟖
x=4
−𝟑𝒙 − 𝟖 = −𝟑𝒙 −𝟖
x+1=5
x+2=6
𝒙𝟐 −𝟐𝒙 − 𝟖 = 𝟎 2 -8-4
-2
𝒙+𝟐 𝒙−𝟒 =𝟎
𝒙+𝟐 =𝟎 𝒙−𝟒 =𝟎
𝒙 = −𝟐
𝒙=𝟒
𝑥
SWBAT: Write a Quadratic Equation and Solve.
Homework Changes
The product of two even consecutive
integers is 120. Find the integers
1.
The product of two consecutive integers is one
less than their sum. Find the integers.
3.
SWBAT: Write a Quadratic Equation and Solve.
Challenge
SWBAT: Write a Quadratic Equation and Solve.
SWBAT: Write a Quadratic Equation and Solve.
Exit Ticket
𝟑 𝑭𝒊𝒓𝒔𝒕
𝟑𝒙
𝟑𝒙
𝟐𝒙
𝒙
𝐹𝑖𝑟𝑠𝑡
𝑥
𝑆𝑒𝑐𝑜𝑛𝑑
Third
𝑥 + 2
𝑥 + 4
= 𝑻𝒉𝒊𝒓𝒅 + 𝟒𝟖
= 𝒙 + 𝟒 + 𝟒𝟖
= 𝒙 + 𝟓𝟐
= 𝟓𝟐
= 𝟐𝟔