27 years ago, Jurassic Park arrived in theaters. Back then, Miss Kito decided to try to capitalize off the success of the movie by selling novelty mosquitos trapped in amber. She called her entrepreneurial endeavor Miss Kito's Mosquitos. She determined that her monthly profit in dollars was determined by the function P(x) = 2000x^2 + 12000x 10000, where x was the price per unit.

There are at least four different methods for finding the vertex of a quadratic function.

Demonstrate two different methods to find the vertex of the Profit function.

If you use your calculator for one of the methods, provide an appropriately labeled sketch of the graph.

(Note that you should get the same answer for both part a and part b, and you are asked to interpret that answer in part c.

Part A: METHOD ONE:

Part B: METHOD TWO:

Part C: What should Miss Kito charge per mosquito in order to maximize her monthly profits? What is the maximum monthly profit?