BACK TO TEXT

2.3b Problem Solving With Quadratics: Homework Exercises

Determine the coordinates of the vertex for the graphs of the following functions.

1.  

2.  

3.   

4.   

5.   

6.   

7.   

8.   

9.   

10.   

Determine the coordinates of the vertex and the intercepts for the following functions.  Then sketch its graph. 

11.   

12.  

13.  

14.  

15.   

16.  

17.   

18.   

19.   

20.   

21. The height above ground of a projectile is measured by the function

    , where  is time in seconds and  is in feet.

    Determine the maximum height achieved by the projectile.

22.   The height of a small rocket fired straight upward is measured by the function          

         where  is measured in feet and t  is measured in seconds.            

        What is the maximum height the rocket will reach?

23.  A ball is thrown vertically upward from the top of a building 96 feet tall with an initial

       Velocity of 80 feet per second.  The height of the ball is measured by the function

       where h(t)  is measured in feet and t is time in seconds.  How

      many feet will the ball travel upward?

24.  The height of a ball thrown straight upward is measured by the function

        where h(t)  is measured in feet and t  is the time in seconds.  

       When is the ball half-way in its trajectory?

25.  A worker on the ground tosses a hammer to a coworker on a scaffold 15 feet above

      the ground.  The initial velocity of the hammer is 32 feet per second.  The height of

      the hammer can be represented by  where h  is measured in feet

      and t is time in seconds.  Will the hammer reach the worker on the scaffold?

26.  A company’s revenue from selling  units of a product is modeled by the function   

    and the cost to produce  units is modeled by the function

   .  and  are measured in thousands of dollars. Determine the  

    number of units the company should produce and sell to maximize its profit. Determine

    the maximum profit.

27.  A  computer dealer has found that his monthly revenue for selling personal computers

      can be modeled by the function   His costs can be

      modeled by   How many computers should he sell monthly to

      achieve the maximum profit?

28.  A store that sells answering machines has determined its costs to be

        and its revenue to be    What is the

      maximum profit the store can make?

29.  A company’s cost function is  and its revenue function is

      where x is in hundreds of units and C(x) and R(x) are in

      thousands of dollars.  Find its maximum profit.

30.  A store selling bicycles has found that its costs can be represented by

        and its revenue by   How many

        bicycles should be sold to maximize profit?  What is the maximum profit?

31.  One number is one less than twice another number.  Their product equals one. Find the

     numbers.

32.  The sum of two numbers is 100.  What is the largest possible product of these

       two numbers?

33.  The average of two numbers is 9.5.  What is the largest possible product of these

       two numbers?

34.  Twice one number minus a  second number is 12.  Find the smallest product of these

       two numbers.

35.  Two numbers differ by .  What is the smallest their product can be?

36.  A farmer has 2400 feet of fencing and wants to enclose a rectangular area.    

      Determine the dimensions of the rectangle that give the maximum area.   What is the

      maximum area?

37.  If the perimeter of a rectangle is 20 feet, what is the largest area it can enclose?

38.  Joan purchased 100 feet of fence.  She plans to create a rectangular garden using

        the side of her garage as one side of the garden and fencing to border the other

        three sides.  What is the maximum area she can enclose?   What dimensions should

        she use for the garden in order to maximize the area?

39.  A boat manufacturer is constructing sails in the shape of a right triangle.  The legs of

      the right triangle must total 36 feet.  What dimensions should he use for the legs in

      order to maximize the surface area of the sail?

40.  An isosceles triangle has a perimeter of 400 and its height is  of either of the equal

       sides.  What would the dimensions need to be to maximize the area of this triangle?

41. Show that the maximum rectangular area enclosed by a finite length of fence must be  

      a square.

                                                                                                                          BACK TO TEXT

ANSWERS TO ODD NUMBERED PROBLEMS

DETAILED SOLUTIONS TO ODD NUMBERED PROBLEMS