Question

First timer please help-

A company plans to sell embroidered hats for $15 each. The company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?
151
401
529
601

Answer 1

I chose 529 but it was wrong. I need to know where I went wrong

Answer 2

you need to construct the quadratic from the given information ...

Answer 3

to find the break even point, sales have to equal costs

Answer 4

15x = cost function

Answer 5

what did you get for your cost function?

Answer 6

I can't remember my teacher took my work. but she told me that one was wrong..

Answer 7

I'm just learning. Im the youngest in the class. should be in 8

Answer 8

well, you have all the information here. how would you construct it? you are given a vertex and a y intercept.

Answer 9

given a vertex, (n,m)

we can construct a vertex form as: y = a(x-m)^2 + n

the y intercept is given so that we can fine tune it: for some y intercept (0,k)

k = a(0-m)^2 + n

k-n = a m^2

(k-n)/m^2 = a

Answer 10

y=15x and y=0.001(150)^2+9000

Answer 11

am I right

Answer 12

my internet is not playing nice :/

Answer 13

7,920 and a vertex of (150, 9,000).

y = a(x-150)^2 + 1000

a = (7920-9000)/(150^2)

y = (7920-9000)(x/150-1)^2 + 1000

the wolf tells me that this is a good assessment of it

y = -6x^2/125 + 72x/5 -80

therefore our setup is:

15x = -6x^2/125 + 72x/5 -80

0 = -6x^2/125 + 72x/5 -15x -80

Answer 14

gonna have to rechk my typing :/

Answer 15

how you get 125

Answer 16

well for starters, i mistyped 1000 instead of 9000 :)

Answer 17

expanding out these big numbers is a pain

Answer 18

:)

Answer 19

y = (7920-9000)(x/150-1)^2 + 9000

y = -1080(x/150-1)^2 + 9000

y = -1080(x^2/150^2 -2x/150 +1) + 9000

y = -1080(x^2/150^2 -x/125 +1) + 9000

y = -1080x^2/150^2 +1080x/125 -1080 + 9000

y = -1080x^2/150^2 +1080x/125 + 7920

thats what im getting without "simplifying"

Answer 20

setting that equal to 15x ... then finding the roots :)

Answer 21

you would find that 400 is one root, so to breakeven they would have to sell 400, to make a profit they would have to sell 401

Answer 22

ok thank you I think I understand now. Thank you Amistre64, gave you a medal

Answer 23

youre welcome, good luck :)

Answer 24

I have another one teacher said was wrong. can you help

Answer 25

she is pointing to kids who were wrong. embarrassing