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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.

Respuesta :

sqdancefan

Answer:

  P = -16(x -28)² +1024

Step-by-step 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

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