Algebra problem help?

blue

A manufacturer determines that the number of drills it can sell is given by the formula D = -4p^2 + 176p -290. where p is the price of the drills in dollars.

a.) At what price will the manufacturer sell the maximum number of drills?

b.) What is the maximum number of drills that can be sold?

thanks in advance (:

kzxsbv

-b/2a is the equation to find the x of a vertex:

(-176 / 2(-4))

simplified:

176/8 = 22

a.) At $22, the max number of drills will be sold.

and for the Y of a vertex, you plug the value into the original equation:

-4(22)^2 + 176(22) - 290 = 1649

(22, 1646)

b.) 1646 is the maximum number that can be sold

http://go.hrw.com/math/midma/gradecontent/manipula...

Plug in your equation with the p's replaced as x in this graphing calculator, then type 21.99 into the "Function Values" under x, then type under that 22, then type under that 22.01 and you'll see that 22 is the max as well.