Advanced Algebra with Trigonometry
Challenge Problem 9
Name
Directions: Show all work and reasoning to receive full credit.
1) A rectangular page is to contain 48 square inches of print. The margins at the top and bottom of the page are
each 1.5 inches. The margins on each side are 1 inch. Find the dimensions of the page that minimize the
amount of paper used by a) drawing a picture to represent the page (with x representing the height of the printed
area and y representing the width of the printed area), b) writing an equation for the area of the page with respect
to one variable, and c) minimizing the area using a graphing utility. (you can round to one decimal place)
2) A ball is thrown from an initial height of 5 feet. After the ball travels 1 foot horizontally, its height is 6.75
feet. Then, after it travels another foot horizontally, the height is 8 feet.
a) Using a graphing utility, find the quadratic equation that best represents the path of the ball.
b) Algebraically find the maximum height the ball will reach.
c) Algebraically find how far the ball will travel horizontally before it hits the ground.