11x1 t11 04 maximum & minimum problems

Maximum/Minimum Problems

Maximum/Minimum ProblemsMaximum/minimum problems involve finding the vertex of a quadratic

Maximum/Minimum ProblemsMaximum/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.

Maximum/Minimum Problems

2e.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.

Maximum/Minimum Problems

2e.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)

Maximum/Minimum Problems

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

23 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)

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

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)

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

21 11

3 46 12

x

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

21 11

3 46 12

x

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

21 11

3 46 12

x

OR 21 4 3 5

59

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

21 11

3 46 12

x

OR 21 4 3 5

59

maximum value

4a

Maximum/Minimum Problems

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

23 5y x x 2 1

3 53

x x

21 1

3 56 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)

21 11

3 46 12

x

OR 21 4 3 5

59

maximum value

4a

5912

114

12

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

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

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

s

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

s

32 s

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

s

32 s 32A s s

(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.

(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.232A s s

(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.232A s s

2 32s s

(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.232A s s

2 32s s

216 256s

(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.232A s s

2 32s s

216 256s

dimensions for a maximum area are 16cm 16cm

(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.232A s s

2 32s s

216 256s

dimensions for a maximum area are 16cm 16cm

Exercise 8E; 1a iv, 2a iii, then multiples of 3