Question

Solve and show work.

The expression P = -x^2 + 6x+ 432 represents a company's profit for selling x items.
(a) for which number(s) of items sold will the company's profit equal 0?
(b) how many items will the company need to sell to maximize profit?

Answer 1

a) to get the profit to equal to 0
-x^2+6x+432=0
divide all by -1 to get rid of the negative in front
x^2-6x-432=0
factor
(x-24)(x+18)=0
x=21,-18
can’t sell -18 items so the answer is
24 ITEMS

b)maximize the profits meaning the maximum points aka. the VERTEX (where the graph is at its highest)
using x=-b/2a formula
you get x=3
to maximize the profit, they need to sell 3 items