035 Completing the Square II Name ______________________________________________ 1. Add to complete the
square here using fully-simplified fractions if necessary.
��2 + 12��______ ��2 + 3��______ ��2
+ 5��______
1
��2 − 2��______
2. Complete the square to convert the following functions to vertex form and then solve them, answering in simplest
radical form if necessary.
��2 + 2�� − 1 ��2 − 8�� + 10 2��2 + 10�� + 10 −��2 − 20�� − 120 3��2 + 21��
+ 35 −��2 + 13�� − 39
3. The profit for a certain company can be represented by the following function: ��(��) = −��2 + 20�� − 15
a. Determine the company’s maximum profit and $ (000s)
the number of items it would have to sell to earn that profit.
b. Determine the breakeven levels of production for this
company in terms of units produced.
(Breakeven is when profit = $0.)
Units (000s)
4. The profit for a certain company can be represented by the following function: ��(��) = −12��2 + 20�� − 150
a. Determine the company’s $ (000s)
maximum profit and the number
of items it would have to sell for that profit.
b. Determine the breakeven levels of production
for this company in terms of units produced.
Units (000s)