Lesson 14.4 Skills Practice
Name
Date
You Must Have a System
Systems of Quadratic Equations
Problem Set
Solve each system of equations algebraically. Then verify each solution graphically.
 
 
y 5 ​x2​ ​2 6x 1 7
 ​ 
​
   ​
1. ​       
y 5 2x
​
y 5 ​x2​ ​2 3x 1 1
 ​ 
​
   ​
2. ​       
y 5 x 2 3
​
y
(7, 14)
14
12
10
8
6
4
2
(1, 2)
0
28 26 24 22
2
4
6
8
x
22
2x 5 ​x2​ ​2 6x 1 7
0 5 ​x​2​2 8x 1 7
0 5 (x 2 7)(x 2 1)
© Carnegie Learning
x 2 7 5 0 or x 2 1 5 0
x 5 7
x51
y 5 2(7)
y 5 2(1)
y 5 14
y52
The system has two solutions:
(7, 14) and (1, 2).
14
Chapter 14 Skills Practice 451448_Skills_Ch14_951-974.indd 969
969
06/06/13 6:01 PM
Lesson 14.4 Skills Practice
 
page 2
 
y 5 ​2x​2​1 6x 2 6
 ​ 
4. ​ ​      
   ​
y 5 3x 1 1
​
© Carnegie Learning
y 5 ​2x​2​1 16x 1 24
 ​ 
​
   ​
3. ​        
y 5 2x 2 2
​
14
970 Chapter 14 Skills Practice
451448_Skills_Ch14_951-974.indd 970
06/06/13 6:01 PM
Lesson 14.4 Skills Practice
page 4
Solve each system of equations algebraically. Then verify each solution graphically.
 
y 5 ​x2​ ​2 2x 1 1
7. ​       
​
  
  ​ ​
y 5 2​x2​ ​ 1 3x 1 4 ​
2​x2​ ​1 3x 1 4 5 ​x2​ ​2 2x 1 1
y
0 5 2​x2​ ​2 5x 2 3
0 5 (2x 1 1)(x 2 3)
8
2x 1 1 5 0 or
6
4
(3, 4)
1 1
2 ,2
2 4
0
28 26 24 22
2
22
24
26
28
4
6
8
x
2x 5 21
1
x 5 2​   ​ 
2
12
1
y 5 ​​ 2​   ​   ​​ ​2 2​ 2​   ​   ​1 1
2
2
1
y 5 ​   ​ 1 1 1 1
4
y 5 ​ 9 ​  5 2​ 1 ​ 
4
4
(  __ )
__ 
__  __ 
__ 
(  __ )
x2350
x53
y 5 (3​)2​ ​2 2(3) 1 1
y592611
y54
(  __  __ )
1
The system has two solutions: ​ 2​   ​ , 2​ 1 ​   ​and (3, 4).
2 4
 
y 5 2​x2​ ​2 x 1 3
8. ​       
​
  ​ ​
​y 5 x​2​1 5x 2 6 ​
© Carnegie Learning
14
972 Chapter 14 Skills Practice
451448_Skills_Ch14_951-974.indd 972
06/06/13 6:01 PM
Lesson 14.4 Skills Practice
Name
page 5
Date
 
y 5 ​x2​ ​2 4x 1 7
9. ​ ​       
  
  ​ ​
y 5 2​x2​ ​2 6x 2 11 ​
 
© Carnegie Learning
y 5 2​x2​ ​1 4x 2 7
 ​ ​
​
  
10. ​       
​y 5 x​2​1 2x 1 1 ​
14
Chapter 14 Skills Practice 451448_Skills_Ch14_951-974.indd 973
973
06/06/13 6:01 PM