# Solving for Maximum / Minimum (Word Problems)

- 1The equation shows the height (h) of a baseball in metres as a function of time (t) in seconds. $$ h=-5t^2+20t+1$$

a) Find the maximum height of the ball and the time when it occurs.

b) What is the initial height of the ball?

c) When does the ball hit the ground?

For more word problems on completing the square, click here - 2The equation shows the height (h) of a ball thrown off a cliff in metres as a function of time (t) in seconds. $$ h=-4.9t^2+29.4t+50$$

a) Find the maximum height of the ball and the time when it occurs.

b) What is the height of the cliff?

c) When does the ball hit the ground? - 3A rectangular enclosure is to be built against a house so that it has three sides. If you have 100 metres of fence, what dimensions will produce a maximum area?
- 4A rectangular kennel is to be enclosed by a fence and divided into two rectangular sections by placing another fence down the middle. If you have 120 metres of fence, what dimensions will produce a maximum area?
- 5Find two integers that have difference of 14 and whose product is a minimum.
- 6A theater usually sells 50 tickets for $30.00 each. For every 1 dollar decrease in price, they sell 5 more tickets. What should the selling price be in order to maximize revenue?

For more word problems on completing the square, click here

$$e=mc^2$$