Please show full solutions! Will mark brainliest for the best answers! Thanks. Question is attached!

9514 1404 393

9514 1404 393

  a)  P = -28(x -112)² +7500

  b) $102.55 or $121.45

Step-by-step explanation:

a) A quadratic relation with a maximum of 7500 at x=112 can be written in vertex form as ...

  P = a(x -112)² +7500

The other given point (x, P) = (89, -7312) can be used to find the value of 'a'.

  -7312 = a(89 -112)² +7500

  -14812 = a(529)

  a = -14812/529 = -28

So, the desired quadratic relation is ...

  P = -28(x -112)² +7500

__

b) The values of x that make P = 5000 can be found from ...

  5000 = -28(x -112)² +7500

  -2500 = -28(x -112)² . . . . . . . . subtract 7500

  89.286 = (x -112)² . . . . . . . . . . . divide by -28

  ±9.45 = x -112 . . . . . . . . . . take the square root

  x = 112 ± 9.45 = {102.55, 121.45}

Setting the price at about $102.55, or $121.45, will yield a profit of $5000.

answer is 33

step-by-step explanation: