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# Quadratic Functions (Word Problems Part 2)

1. 1
The equation shows the height (h) of a baseball in metres as a function of time (t) in seconds. $$h=-5t^2+40t+1$$ What was the maximum height?
At what time did the ball reach its maximum height?
What is the height of the ball after 1 second?
What was the initial height of the ball?
At what time does the ball hit the ground?

2. 2
The equation shows the height (h) of a ball in metres as a function of time (t) in seconds. $$h=-4.9t^2+147t+10$$ What was the maximum height?
At what time did the ball reach its maximum height?
What is the height of the ball after 2 seconds?
What was the initial height of the ball?
At what time does the ball hit the ground?

3. 3
An astronaut throws a rock on the moon. The equation shows the height (h) of the rock in metres as a function of time (t) in seconds. $$h=-0.8t^2+8t+5$$ What was the maximum height?
At what time did the rock reach its maximum height?
What is the height of the rock after 1 second?
What was the initial height of the rock?
At what time does the rock hit the ground?

4. 4
An astronaut kicks a ball on mars. The equation shows the height (h) of the ball in metres as a function of time (t) in seconds. $$h=-2t^2+20t$$ What was the maximum height?
At what time did the ball reach its maximum height?
What is the height of the ball after 6 seconds?
Was the ball moving up or down at 6 seconds?
What was the initial height of the ball?
At what time does the ball hit the ground?

5. 5
The equation shows the height of a rocket, h metres, as a function of the horizontal distance, d metres, the rocket travels from the launch pad until it hits the ground. $$h=-0.03d^2+0.36d+4$$ What was the maximum height?
At what distance from the launch pad did the rocket reach its maximum height?
What is the height of the rocket at 4 metres from the launch pad?
What was the initial height of the rocket?
At what distance from the launch pad does the rocket hit the ground?

6. 6
A rectangular enclosure is to be built against a wall so that it has three sides. If you have 80 metres of fence, what dimensions will produce a maximum area?
7. 7
A rectangular enclosure is to be built against a house so that it has three sides. If you have 120 metres of fence, what dimensions will produce a maximum area?
8. 8
A kennel wants to build a rectangular enclosure with a fence in the middle so that two dogs can have separate areas. If 120 metres of fence is available, find the dimensions of the enclosure that will produce a maximum area.
9. 9
A shop usually sells 200 sandwiches for $5.00 each. For every 50 cent increase in price, they sell 10 fewer sandwiches. What should the selling price be in order to maximize revenue? 10. 10 A theater usually sells 100 tickets for$50.00 each. For every 1 dollar decrease in price, they sell 5 more tickets. What should the selling price be in order to maximize revenue?
11. 11
Find two integers that have difference of 10 and whose product is a minimum.
12. 12
Find two integers that have difference of 12 and whose product is a minimum.

$$e=mc^2$$