Height of the Ball
Date: 01/05/98 at 01:29:03 From: Lesley Trupiano Subject: Algebra II Word Problem Dear Dr. Math, This question involves a "model," a concept that is hard for me to understand. The question is: A football player kicked a 41-yard punt. The path of the ball was modeled by y= -0.035x(squared) + 1.4x + 1, where x and y are measured in yards. What was the maximum height of the ball? The player kicked the football toward midfield from the 18 yard line. Over which yard line was the ball when it was at its maximum height? Basically I have problems with this because I know a) nothing about football whatsoever, and b) I don't understand how to tell where the maximum height of the ball is on my graph. I've plugged the equation into my calculator, but I still can't see how to do this. Any help would be much appreciated! Thanks, Lesley
Date: 01/05/98 at 10:07:25 From: Doctor Rob Subject: Re: Algebra II Word Problem First of all, a model is a mathematical equation (or a set of several mathematical equations) which describe some real, physical situation. In this case, x measures the number of yards along the field from the point where the ball was kicked, and y measures the number of yards above the field the ball is. One way to find the maximum is by completing the square. Write y = -0.035*(x - a)^2 + b for some constants a and b. The maximum value of y will occur when the square is least. Since squares are always nonnegative, the square is least when it is zero. Then the maximum will occur when x = a, and the maximum value will be y = b. Since the ball was kicked from the 18-yard line, the answer to the second part will be 18 + a. If you do not understand how to complete the square, write back again and we will try to answer that. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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