Download Precalculus

Precalculus
Quadratic Applications #1
Name _______________________________
Be sure to include the following:
* A relevant picture or figure.
* A let statement defining any variables.
* An equation that will be solved.
* All relevant work.
* A solution to the variable
* A concluding statement that answer the original question.
1. Two numbers add to 5. What is the largest possible value of their product?
2. The difference of two numbers is 1. What is the smallest possible value for the sum of their squares?
3. What is the largest possible area for a rectangle with a perimeter of 80 cm?
4. A farmer has 800 feet of fencing to enclose a rectangular field. What is the maximum area he can
enclose? What are the dimensions of the field?
5. A baseball is thrown straight up, and its height as a function of time is given by the formula
ht   16t 2  32t (where h is in feet and t is in seconds).
a) Find the height of the ball when t = 1 sec and when t = 3/2 sec.
b) Find the maximum height of the ball and the time at which the height is attained.
c) At what times is the height 7 feet?
6. a) What number exceeds it square by the greatest amount?
b) What number exceeds twice its square by the greatest amount?