Question

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

f(x)=−2(x+105)2+18,050
f(x)=−2(x−105)2+18,050
f(x)=−10(x+105)2+18,050
f(x)=−10(x−105)2+18,050

Answer 1

We want a parabola in vertex form f(x)=a(x−h)^2+k with vertex (h,k) = (105, 18050). Use the point (10,0) to find a:

0 = a(10−105)^2 + 18050 = a(−95)^2 + 18050 = a(9025) + 18050
a = −18050/9025 = −2

So f(x) = −2(x−105)^2 + 18,050.