The profit, P (in thousands of dollars), that a company makes selling an item is a quadratic function of the price, x (in dollars), that they charge for the item. The following expressions for P(x) are equivalent:

P(x) = 2x² + 24x - 54
P(x) = -2(x − 3)(x − 9)
P(x) = −2(x − 6)² + 18

a. Which of the equivalent expressions for P(x) reveals the price which gives a profit of zero without changing the form of the expression?
P(x) = 2x² + 24x - 54
P(x) = -2(x-3) (x-9)
P(x) = -2(x − 6)² + 18

b. Find a price which gives a profit of zero.​