1. A flare is launched into the air. The path of the flare can be modelled by the equation h = 0.1(d - 10)^2 + 25, where h is the height of the flare and d is the horizontal distance of the flare from where it was fired, both in metres.

a) What is the vertex of the relation, and what do these coordinates represent?

b) From what initial height was the flare fired?

2. A baseball is hit in the air. Its path can be modelled by the relation h = -2(d - 2)^2 + 33, where h is the height of the ball and d is the horizontal distance, both in metres.

a) What is the vertex of this relation?

b) What is the maximum height of the ball?

c) What does the coordination of the vertex represent in this situation?

d) What is the height of the ball when it has travelled a horizontal distance of 6m?

3. The revenue of an item can be modelled by the relation R = -40(x - 21)^2 +60 840 where R is revenue and x represents the number of items sold.

a) What is the vertex of the parabola?

b) What do the coordinates of the parabola represent?

4. A pebble is fired from a slingshot from the top of a small hill. The path of the pebble can be modelled by the equation h = -5.25(t - 4)^2 + 96, where h is the height of the pebble in metres and t is the time in seconds after the pebble was fired.

a) Find the vertex of the parabola.

b) How long will the pebble take to reach its maximum height?

c) What is the maximum height?

d) What is the height of the small hill?

5. A golf ball is hit from the top of a cliff and fell to the green located at the bottom of the valley. The path of the golf ball can be modelled by the relation h = -05(t - 5)^2 + 60 where h is height in metres above the valley and t is the time after the ball was hit, in seconds.

a) what is the maximum height of the golf ball?

b) How long does it take the golf ball to reach its maximum height?

c) What is the height of the ball after 3 seconds?

d) What is the height of the cliff?

6. A football is thrown into the air. Its path can be modelled by the equation h = -0.19)d - 16)^2 + 57, where h is the height of the ball and d is the horizontal distance, both in metres.

a) What is the vertex of this relation?

b) What is the maximum height of the ball?

c) What does the coordination of the vertex represent in this situation?

d) What is the height of the ball when it has travelled a total horizontal distance of 8m?

e) How high is the quarterback that throws the football?

7. An arrow is shot from the top of a platform. The path of the arrow can be modelled by the equation h = -0.005(t - 26)^2 + 5, where h is the height of the arrow in metres and t is the time in seconds after the arrow was shot.

a) Find the vertex of the parabola.

b) How long will it take the arrow to reach its maximum height?

c) What is the maximum height?

d) what is the height of the platform?