1. For each quadratic, determine the number of roots. Find the vertex.
a)
f ( x )   2 x  2 x  12
b)
f ( x )  x  6 x  10
c)
f (x)  x  6x  5
d)
f (x)  x  6x  9
e)
f (x)   x  2 x  8
2
2
2
2
2
2. A manufacturter finds his monthly fixed costs total $830 and each unit costs an additional $60
to produce. Demand quantity for the product is 0 unless the price is below $107. For each
decrease of $6 in the price he is able to sell 30 more units.
a) Graph the cost, revenue and profit functions in the same window.
b) Find the break even quantities.
c) Find the quantity for maximum profit and the max. profit.
d) What is the demand price at the quantity for max. profit.
3. Equilibrium. For a certain product, 1000 units can be sold at a price of $20.00 per unit. For
each increase of $2.00 in the price, 100 fewer can be sold. Suppliers will provide only 670 units
if the price is $20.00 and will provide none if the price is $13.30 or lower.
Find the equilibrium quantity and price.