Maximum/minimum problems involve finding the vertex of a quadratic function. It is important to read the question carefully to determine if you need to find the x-value or y-value of the vertex. To find the maximum/minimum, you set the derivative of the function equal to 0 and solve for the x-value of the vertex, then substitute this back into the original function to find the y-value at the vertex.

1. Maximum/Minimum Problems

2. Maximum/Minimum Problems
Maximum/minimum problems involve finding the vertex of a quadratic

3. Maximum/Minimum Problems
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.

4. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.

5. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)

6. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)

7. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)

8. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)

9. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)
2
1 11
3 4
6 12
x
 
    
 

10. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
11
maximum value is 4
12
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)
2
1 11
3 4
6 12
x
 
    
 

11. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
11
maximum value is 4
12
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)
2
1 11
3 4
6 12
x
 
    
 
OR   2
1 4 3 5
59
    
 

12. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
11
maximum value is 4
12
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)
2
1 11
3 4
6 12
x
 
    
 
OR   2
1 4 3 5
59
    
 
maximum value
4a



13. Maximum/Minimum Problems
2
e.g. ( ) Find the maximum value of 3 5i y x x   
2
3 5y x x   
2 1
3 5
3
x x     
 
2
1 1
3 5
6 12
x
 
     
 
11
maximum value is 4
12
 
Maximum/minimum problems involve finding the vertex of a quadratic
Read the question carefully to see if it is the x value or the y value you
are required to find.
(Need to find the y value of the vertex)
2
1 11
3 4
6 12
x
 
    
 
OR   2
1 4 3 5
59
    
 
maximum value
4a


59
12
11
4
12


 

14. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?

15. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?

16. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s

17. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s

18. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 

19. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.

20. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.
2
32A s s 

21. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.
2
32A s s 
 2
32s s  

22. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.
2
32A s s 
 2
32s s  
 
2
16 256s   

23. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.
2
32A s s 
 2
32s s  
 
2
16 256s   
dimensions for a maximum area are 16cm 16cm 

24. (ii) A rectangle has perimeter of 64 cm.
What dimensions would the rectangle have for maximum area?
s
32 s
 32A s s 
We want the dimensions, so it is the
x value of the vertex we need to find.
2
32A s s 
 2
32s s  
 
2
16 256s   
dimensions for a maximum area are 16cm 16cm 
Exercise 8E; 1a iv, 2a iii, then multiples of 3