Question

Pauline wants to sell stainless steel water bottles as a school fundraiser.

She knows that she will maximize profits, and raise $1024, if she sells

the bottles for $28 each. She also knows that she will lose $4160 if she sells the bottles for only $10 each.

Write a quadratic relation to model her profit, P, in dollars, if she sells the bottles for x dollars each.

Answer 1

P = -16(x -28)² +1024

Explanation:

The equation can be written in vertex form as ...

P = -a(x -h)² +k

where (h, k) is the vertex, and 'a' is a scale factor. We are given the vertex (h, k) = (28, 1024) and another point (x, P) = (10, -4160). Using these points, we can find the value of 'a'.

-4160 = -a(10 -28)² +1024

-5184 = -324a . . . . simplilfy

a = 5184/324 = 16 . . . . divide by the coefficient of 'a'

A suitable quadratic relation is ...

P = -16(x -28)² +1024