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Intersection of Quadratic and Linear Functions

In this worksheet, students find the intersection of quadratic and linear functions using graphs. Graph paper will be needed.

'Intersection of Quadratic and Linear Functions' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Recognise, Sketch and Interpret Graphs of Linear/Quadratic/Cubic/Reciprocal Functions

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about calculating the intersection of quadratic and linear functions.

 

Example

Use the graphs of y=x2+2x-3  and y=6 to solve x2+2x-3=6

You should get two answers each time (in this example x1=-4.2, x2=2.2).

This is the solution to the pair of simultaneous equations:
y = x2 + 2x - 3
y = 6

Solve this pair of simultaneous equations:

y = x2 +8x +7
y=3

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-7.5
7.5
0.5
-0.5

Solve this pair of simultaneous equations:

y = x2+2x -7
y=7

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-10.2
7.5
2.9
-4.9

Solve this pair of simultaneous equations:

y = x2-7x-7
y=1

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-1
7.5
0.5
8

Solve this pair of simultaneous equations:

y = x2 -5x +6
y=2

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
1
2
3
4

Solve this pair of simultaneous equations:

y = x2 -8x +8
y=6

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
0.1
7.7
0.3
7.4

Solve this pair of simultaneous equations: 

y = x2 -x -10
y=2

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
4
7.7
-3
7.4

Solve this pair of simultaneous equations: 

y = x2 -6x + 5
y=5

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-4
0
-3
6

Solve this pair of simultaneous equations:

y = x2 + 9x - 4
y=4

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-4
0.8
-9.8
6

Solve this pair of simultaneous equations:

y = x2 - 2x - 4
y=7

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-4
-2.5
-9.8
4.5

Solve this pair of simultaneous equations:

y = x2 + 2x - 3
y=6

x1 =
 
x2 =
 

 

Note that x1 < x2

 x1x2
-4.2
-2.5
-9.8
2.2
  • Question 1

Solve this pair of simultaneous equations:

y = x2 +8x +7
y=3

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-7.5
7.5
0.5
-0.5
  • Question 2

Solve this pair of simultaneous equations:

y = x2+2x -7
y=7

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-10.2
7.5
2.9
-4.9
  • Question 3

Solve this pair of simultaneous equations:

y = x2-7x-7
y=1

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-1
7.5
0.5
8
  • Question 4

Solve this pair of simultaneous equations:

y = x2 -5x +6
y=2

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
1
2
3
4
  • Question 5

Solve this pair of simultaneous equations:

y = x2 -8x +8
y=6

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
0.1
7.7
0.3
7.4
  • Question 6

Solve this pair of simultaneous equations: 

y = x2 -x -10
y=2

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
4
7.7
-3
7.4
  • Question 7

Solve this pair of simultaneous equations: 

y = x2 -6x + 5
y=5

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-4
0
-3
6
  • Question 8

Solve this pair of simultaneous equations:

y = x2 + 9x - 4
y=4

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-4
0.8
-9.8
6
  • Question 9

Solve this pair of simultaneous equations:

y = x2 - 2x - 4
y=7

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-4
-2.5
-9.8
4.5
  • Question 10

Solve this pair of simultaneous equations:

y = x2 + 2x - 3
y=6

x1 =
 
x2 =
 

 

Note that x1 < x2

CORRECT ANSWER
 x1x2
-4.2
-2.5
-9.8
2.2
---- OR ----

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