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Homework: Solving Problems by Graphing Quadratic Functions

Module by: Kenny M. Felder. E-mail the author

Summary: Some homework problems involving graphing quadratic functions.

Just as we did in class, we will start with our old friend

h(t)=ho+vo−16t2h(t)=ho+vo−16t2 size 12{h \( t \) =h rSub { size 8{o} } +v rSub { size 8{o} } - "16"t rSup { size 8{2} } } {}.

Exercise 1

Michael Jordan jumps into the air at a spectacular 24 feet/second.

  • a. Write the equation of motion for the flying Wizard.
  • b. Put that equation into standard form for graphing, and draw the graph as before.
  • c. How long does it take him to get back to the ground?
  • d. At what time does His Airness reach his maximum height?
  • e. What is that maximum height?

Exercise 2

Time to generalize! A ball is thrown upward from the ground with an initial velocity of vovo size 12{v rSub { size 8{o} } } {}. At what time does it reach its maximum height, and what is that maximum height?

Some more problems from my Calculus books.

Exercise 3

Find the dimensions of a rectangle with perimeter 100 ft whose area is as large as possible. (Of course this is similar to the one we did in class, but without the river.)

Exercise 4

There are lots of pairs of numbers that add up to 10: for instance, 8+28+2 size 12{8+2} {}, or 912+12912+12 size 12{9 { {1} over {2} } + { {1} over {2} } } {}. Find the two that have the largest product possible.

Exercise 5

A pharmaceutical company makes a liquid form of penicillin. If they manufacture xx size 12{x} {} units, they sell them for 200 xx size 12{x} {} dollars (in other words, they charge $200 per unit). However, the total cost of manufacturing xx size 12{x} {} units is 500,000+80x+0+0.003x2500,000+80x+0+0.003x2 size 12{"500","000"+"80"x+0+0 "." "003"x rSup { size 8{2} } } {}. How many units should they manufacture to maximize their profits?

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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