# Linear Quadratic Functions Worksheet by chenmeixiu

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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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