Profit (in thousands of dollars) company makes from selling the definite item relies on cost of item. Three different forms of profit function at the price of p dollars are:
standard form: -2p2 +24p-54
factored form: -2(p-3)(p-9)
vertex form:-2(p-6)2 +18
(a) Illustrate that three forms are equivalent.
standard form: -2p2 + 24p -54
factored form:-2 (p-3)(p-9)
vertex form: -2(p-6)2+18
(b) Which form is most helpful for finding prices which give the profit of zero dollars?(These are known as break-even prices.) Utilize form you select to find prices. Write the sentence in English explaining what points mean in context.
(c) Which form is most helpful for determining profit when price is zero? Use it to determine that profit. Describe what this might mean in context of problem.
(d) Company would like to maximize profits. Which form is most helpful for computing price which provides maximum profit? Use it to estimate best price and profit made at that price.