Linear Quadratic Functions Worksheet

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					Linear / Quadratic Functions Worksheet

   1.     As a salesperson for Trading Cards Unlimited, Justin receives a monthly base
          pay plus commission on all that he sells. If he sells $600 worth of
          merchandise in one month, he is paid $350. If he sells $900 worth of
          merchandise in one month, he is paid $425.

          a ) Find Justin’s total salary function s( x ) when he sells x dollars of
          merchandise.

                350  425  75 1
           m                 
                600  900  300 4


           s( x) 
                  1
                    x  600  350
                  4
           sx   x  150  350
                  1
                  4
           sx   x  200
                  1
                  4

              b) Using that function, find Justin’s salary when he sells $2,900 worth of
              merchandise

               s2900    2900  200
                         1
                         4
               s2900  725  200
               s2900  925

   2.     Wacky Widget Inc. makes widgets used in computers. To produce 100
          widgets, it costs the company $250. To produce 500 widgets it costs the
          company $500.

          a ) Find the cost function c(x) for producing x number of widgets

                250  500  250 5
          m                  
                100  500  400 8


          c( x) 
                 5
                   x  100  250
                 8
                 5
          c( x)  x  62.5  250
                 8
                 5
          c( x)  x  187.5
                 8
     b ) Using that function, find the cost to produce 425 widgets.

         c425    425  187.5
                  5
                  8
         c425  265.63  187.5
         c425  $453.13

3.   Photo Necessities produces camera cases. The company has discovered it
     costs $23 to produce 2 cases, $103 to produce 4 cases, and $631 to produce 10
     cases.

     a) find the cost function c(x) to produce x camera cases.
                     23  a2  b2  c                        23  4a  2b  c
                              2
         EQ 1                                            EQ 1
                    103  a4  b4  c                       103  16a  4b  c
                              2
         EQ 2                                            EQ 2
                    631  a10  b10  c                     631  100a  10b  c
                                  2
         EQ 3                                            EQ 3
            EQ 2 – EQ 1 = EQ 4                                     EQ 3 – EQ 2 = EQ 5
           103  16 a  4b  c                       631  100 a  10 b  c
          23  4a  2b  c                        103  16 a  4b  c
            80  12 a  2b                            528  84 a  6b
               EQ 4                                       EQ 5

     Use addition method with EQ 4 and EQ 5
     EQ 4 - 380  12a  2b 
     EQ 4  240  36a  6b
     EQ 5     528  84a  6b
             288  48a
                a6


     Substitute a  6 into 80  12a  2b to find b
     80  126   2b
     80  72  2b
     8  2b
     b4

     Substitute a  6 and b  4 into 23  4a  2b  c to find c
     23  46   24   c
     23  24  8  c
     23  32  c
     c  9


     Using a  6, b  4, c  9       c( x)  6 x 2  4 x  9
     b) Find the total cost of producing 8 camera cases
         cx   6 x 2  4 x  9
         c8  68  48  9
                      2


         c8  664  32  9
         c8  384  32  9
         c8  407

4.   A ball is launched from a slingshot. Its height h(t) can be measured by a
     quadratic equation in terms of time ( t ) in seconds.

     After 1 second, the ball is 76 feet in the air. After 2 seconds, the ball is 144
     feet in the air.

     a) Find the height function h(t) for the slingshot.

                0  a 0   b0  c              0c
                            2
     EQ 1
               76  a1  b1  c              76  1a  1b
                            2
     EQ 2
     EQ3 144  a2   b2   c                144  4a  2b
                            2




     Use addition method on Eq 2 and EQ 3
      276  1a  1b 
      152  2a  2b
       144  4a  2b
         8  2a
          a  4

     Substitute a  4 into EQ2 and find b

     76  1- 4   1b 
     76  4  b
     b  80


     Substituting a  4, b  80, c  0 into h(t )  at 2  bt


     h(t )  4t 2  80t
     b) Find the height of the ball after 8 seconds in the air.

         ht   4t 2  80t
         h8  48  808
                        2


         h8  256  640
         h8  384 feet

5.   Clucks Calculators Inc. produces calculators for schools. The company has
     discovered that it costs $18 to produce 2 calculators, $66 to produce 4
     calculators, and $450 to produce 10 calculators.

     a) Find the cost equation C(x) of producing x calculators.
             18  a 2   b2   c           18  4a  2b  c
                        2
     EQ 1                              EQ 1
               66  a 4   b4   c               66  16a  4b  c
                            2
     EQ 2                                    EQ 2
     EQ 3 450  a 10  b10  c           EQ 3 450  100a  10b  c
                                2




     EQ 2  EQ 1                            EQ 3  EQ 2
       66  16a  4b  c                      450  100a  10b  c
      18  4a  2b  c                       - 66  16a  4b  c
      48  12a  2b ( EQ 4 )                  384  84a  6b ( EQ 5 )


     Use addition method to find " a" with EQ' s 4 & 5
         384  84a  6b              384  84a  6b
       348  12a  2b            144  36a  6b
                                         240  48a
                                          a5


     Substitute a  5 into 48  12a  2b to find " b"
     48  125  2b
     45  60  2b
      12  2b  b  6


     Substitute a  5 and b  6 into 18  4a  2b  c to find " c"
     18  45  2 6   c
     18  20  12  c
     18  8  c
     c  10


     Substitute a  5, b  6, c  10 into c( x)  ax 2  bx  c
     c( x)  5 x 2  6 x  10
b) Find the cost of producing 25 calculators.

    c x   5 x 2  6 x  10
    c25  525  625  10
                    2


    c25  5625  150  10
    c25  3125  150  10
    c25  2985

				
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