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