Quadratic Problems

• The sides of an existing square warehouse are to be extended by 5 metres

• and 8 metres. The area of the new extended warehouse will be 340m2. The existing warehouse (shaded) and planned extension are shown in the diagram below.

Solve the equation (x + 8)(x + 5) = 340 to find the new dimensions.

Solve the equation (x + 8)(x + 5) = 340 to find the new dimensions.

Cannot have a negative so x = 12

Old dimensions 12m x 12mNew dimensions 20m x 17m

• A ball bearing rolls down a slope labeled AB. The time, t seconds, for the ball bearing to reach B is the solution to the equation

• t2 + 5t = 36.How long does it take for the ball bearing to reach B?

T = 4 as you can’t have negative time

A field is 40 m longer than it is wide. The area of the field is 3200 m2 What is the length and width of the field?

x

x + 40

A field is 40 m longer than it is wide. The area of the field is 3200 m2 What is the length and width of the field?

x

x + 40

A field is 40 m longer than it is wide. The area of the field is 3200 m2 What is the length and width of the field?

x

x + 40

The length is 80m and width is 40m

x

x + 40

• A golf ball is hit into the air. Its flight can be calculated by the equation: h=40t-8t2 where

• h=height from the ground • And t=time in the air. • Find the time taken for the ball to reach a

height of 48 metres.Explain why there are two possible values.

• A golf ball is hit into the air. Its flight can be calculated by the equation: h=40t-8t2 where

• h=height from the ground • And t=time in the air. • Find the time taken for the ball to reach a

height of 48 metres.Explain why there are two possible values.

• A golf ball is hit into the air. Its flight can be calculated by the equation: h=40t-8t2 where

• h=height from the ground • And t=time in the air. • Find the time taken for the ball to reach a

height of 48 metres.Explain why there are two possible values.

The height is modelled by a parabola and hence it will reach 48 metres on

the way up and again on the way down.

• To find two positive consecutive odd integers whose product is 99 we can use the following logic:

• x is the first integer • x + 2 is the second integer • therefore x(x + 2) = 99 Continue with the logic

to find the answer.

• To find two positive consecutive odd integers whose product is 99 we can use the following logic:

• x is the first integer • x + 2 is the second integer • therefore x(x + 2) = 99 Continue with the logic

to find the answer.

The integers are 9 and 11

• To find two positive consecutive odd integers whose product is 99 we can use the following logic:

• x is the first integer • x + 2 is the second integer • therefore x(x + 2) = 99 Continue with the logic

to find the answer.