4.15 Homework: solving problems by graphing quadratic functions

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?

Time to generalize! A ball is thrown upward from the ground with an initial velocity of $v_o$ . At what time does it reach its maximum height, and what is that maximum height?

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.)

There are lots of pairs of numbers that add up to 10: for instance, $8+2$ , or $9\frac{1}{2}+\frac{1}{2}$ . Find the two that have the largest product possible.

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