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
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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5

5. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)

6. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5

7. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5
 3  x 2  x   5
1
 
 3 

8. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5
 3  x 2  x   5
1
 
 3 
2
x 1 1
 3    5
 6  12

9. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5
 3  x 2  x   5
1
 
 3 
2
x 1 1
 3    5
 6  12
2
 3  x    4
1 11
 
 6 12

10. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5
 3  x 2  x   5
1
 
 3 
2
x 1 1
 3    5
 6  12
2
 3  x    4
1 11
 
 6 12
11
 maximum value is  4
12

11. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5 OR   12  4  3 5 
 3  x 2  x   5
1  59
 
 3 
2
x 1 1
 3    5
 6  12
2
 3  x    4
1 11
 
 6 12
11
 maximum value is  4
12

12. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5 OR   12  4  3 5 
 3  x 2  x   5
1  59
  
 3 
maximum value 
x 1
2
1 4a
 3    5
 6  12
2
 3  x    4
1 11
 
 6 12
11
 maximum value is  4
12

13. 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.
e.g. (i ) Find the maximum value of y  3 x 2  x  5
(Need to find the y value of the vertex)
y  3 x 2  x  5 OR   12  4  3 5 
 3  x 2  x   5
1  59
  
 3 
maximum value 
x 1
2
1 4a
 3    5 59
 6  12 
2 12
 3  x    4
1 11
  11
 6 12  4
11 12
 maximum value is  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
A  s  32  s 
32  s

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

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

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

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