math 2 Key Features of Quadratics

Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-6x^2+600x-5726 y=−6x 2 +600x−5726

Answer 1

y(x) =-6x^2 +600x -5726

using differential calculus

y' =-12x +600 =0

x =600/12 = 50

max profit = y(50)

= -6(50)^2 +600(50) -5726

= -6(2500) + 30000 -5726

=-15,000 +30,000- 5726

= 15000 -5726

=$9,274

or use algebra, geometry as the function is a downward opening parabola

y=-6x^2 +600x -5726

complete the square

-6(x^2 -100x + 50^2) = 5726 -6(50^2)

-6(x-50)^2 = 5726 -15000= -9274

-6(x-50)^2 = 9274

in vertex form, vertex = (50, 9276)

x= 50 is the x value that maximizes y= $9,276,