Max/Min Problems With Equations Worksheet



Quadratic word problems Worksheet

Complete each question on lined paper

1. Red aerial mini-flares are used by some boaters in an emergency. The flight of one brand of flare, when fired at a angle of 70° to the horizontal is modelled by the function [pic], where h is the height, in metres and t is the time, in seconds, since the flare was fired.

a) State the vertex.

b) State whether it is a max or a min.

c) What is the max/min height reached?

d) When was the max/min height reached?

e) What is the height reached after 4 seconds?

2. The following function gives the heights, h metres, of a batted baseball as a function of the time, t seconds, since the ball was hit.

[pic]

a) State the vertex.

b) State whether it is a max or a min.

c) What is the max/min height reached?

d) When was the max/min height reached?

e) What is the height reached after 1 second?

3. A stone is thrown into the air from a bridge over a river. The stone falls into the river. The height ‘h’ above the river, of the stone in metres, ‘t’ seconds after it is thrown is given by: [pic]

a) When does the stone hit the river?

b) What is the maximum height of the stone?

c) What is the height of the bridge?

4. The height of an infield fly ball, ‘h’ metres, ‘t’ seconds after it is hit is given by the equation: [pic]

a) How long does it take for the ball to hit the ground? (assuming that is not caught)

b) What is the maximum height of the ball?

c) How high is the ball after 4 seconds?

d) For c) above, is the ball on the way up or on the way down?

5. An Acapulco diver dives into the sea from a cliff. His height ‘h’ in metres, ‘t’ seconds after leaving the cliff is given by: [pic].

a) How high is the cliff?

b) How long is it until he reaches the water?

Answers

1 a) (3,83) b) max c)83 m d) 3 sec e) 72 m

2 a) (2.5,38.5) b) max c) 38.5 m d) 2.5 sec e) 25

3. a) 5 seconds b) 61.25 m c) 50 m

4. a) 8 seconds b) 125 m c) 120 m d) on the way down

5. a) 35 m b) 1 second

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