4.2+Measuring+Jumps

February 10, 2009 SO =__Quadratic functions can help us describe situations in the real world.__=

__How can I make a prediction using quadratic relationships?__
==A. Use your calculator to make tables, and graphs of these three equations. Since a jump doesn't take much time, look at heights for time values between 0 seconds and 1 second. In your tables, use intervals of 0.1 second.== The basketball players maximum height was 10.5 feet and he reached it at .5 sec. The frog's maximum height was 2.26 feet and he reached it at .4 sec. The fleas maximum height was .96 feet and he reached it at .2 sec.
 * Time (sec.) || Frog || Flea || Basketball Player ||
 * 0 || .02 || 0 || 6.5 ||
 * .1 || 1.06 || .64 || 7.94 ||
 * .2 || 1.78 || .96 || 9.06 ||
 * .3 || 2.18 || .96 || 9.86 ||
 * .4 || 2.26 || .64 || 10.34 ||
 * .5 || 2.02 || 0 || 10.5 ||
 * .6 || 1.46 || -.96 || 10.34 ||
 * .7 || .58 || -2.24 || 9.86 ||
 * .8 || -.62 || -3.84 || 9.06 ||
 * .9 || -2.14 || -5.76 || 7.94 ||
 * 1 || -3.98 || -8 || 6.5 ||
 * B. What is the maximum height reached by each jumper, and when is the maximum height reached?**

The Basketball players jump lasted for the full second. The frogs jump lasted for .7 seconds. The fleas jump lasted for .5 seconds. I found this by looking at my table and when the numbers became negative I knew they had already landed because it is not possible to go below the ground.
 * C. How long does each jump last? Explain how you found your answer.**

They tell you about the basketball player and the frog because that is how high off the ground they were.
 * D. What do the constant terms 0.2 and 6.5 tell you about the frog and the basketball player?**

Follow up The pattern of change for each of the jumpers is as time increases so does height but then height decreases. a. Make a table and a graph for this equation.** b. What do the equation, the table, and the graph suggest about the relationship between price and profit?** They suggest that as the price goes up, so does the profit. But at a certain point it goes down. $25 will bring in the most profit. This equation compares to the equations in4.2 because they are both parabola's on a graph but this equation has a positive number not a negative one.
 * 1. For each jumper, describe the pattern of change in the height over time, and explain how the pattern is reflected in the table and the graph.**
 * 2. Mr Jain is a jewelry maker. He would like to increase his profit by raising the price of his jade earrings. However, he knows that if he raises the price too high, he won't sell as many earrings and his profit will decrease. Using records of past sales, a business consultant developed the equation P = 50s - s^2 to predict the monthly profit, P, for a given sales price, s.
 * x price || y profit ||
 * 0 || 0 ||
 * 1 || 49 ||
 * 2 || 96 ||
 * 3 || 141 ||
 * 4 || 184 ||
 * 5 || 225 ||
 * 6 || 264 ||
 * 7 || 301 ||
 * 8 || 336 ||
 * 9 || 369 ||
 * 10 || 400 ||
 * 11 || 429 ||
 * 12 || 456 ||
 * 13 || 481 ||
 * 14 || 504 ||
 * 15 || 525 ||
 * 16 || 544 ||
 * 17 || 561 ||
 * 18 || 576 ||
 * 19 || 589 ||
 * 20 || 600 ||
 * 21 || 609 ||
 * 22 || 616 ||
 * 23 || 621 ||
 * 24 || 624 ||
 * 25 || 625 ||
 * [[image:Graph_2_shea.png]]
 * c. What price will bring the greatest profit?**
 * How does this equation compare with the equations in problem 4.2?**