Question

Will Give Medal!!!

The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem?
Part B: Determine the x-intercepts. What do these values mean in the context of the problem?

Answer 1

do youknow how to find vertex?

Answer 2

Yes im pretty sure lol

Answer 3

so what is it?

Answer 4

Well first dont we have to put it in vertex form? Or can you find it without doing that...?

Answer 5

yes y = a(x - h)2 + k

Answer 6

thats the formula

Answer 7

Right so its in vertex form?

Answer 8

n you have to plug it in the formula

Answer 9

no

Answer 10

Oh ok so ow do you do that?

Answer 11

you havent learned that?

Answer 12

no... it wasnt in my lesson at least...

Answer 13

You can see from the chart that function #2 has a minimum value of (-1,-3). We know this because the x values on either side of -1, -2 and 0, provide us with y values that are greater than -3.

Now that we know what the minimum value is for function #2, we need to find the minimum for function #1. We can do this by using the first bit of the quadratic formula (-b/2a). Plugging in function #1 gives us (8/4) or 2. This represents the x value of the vertex. Plugging 2 into function #1 gives us an answer of -7, or a vertex of (2,-7).

Now that we know both vertices, we can see that, since -7 is smaller than -3, function #1 has the least minimum value, occurring at (2,-7)

Answer 14

what chart deadpool?

Answer 15

yea im a little confused... lol

Answer 16

@-Deadpool-

Answer 17

So i found the vertex and it is (25,361)

Answer 18

my bad cheerleader I did not mean to say chart, i think i might have read the question wrong lol

Answer 19

thats correct so
The vertex represents the maximum possible profit of 361 dollars by selling 25 memberships.
.

Answer 20

now part b

Answer 21

ok

Answer 22

first factor out the negative sign
−(x2−50x+264)

Answer 23

so we have (x2−50x+264)

Answer 24

Which two numbers add up to -50 and multiply to 264?

Answer 25

@Hannahwaller5

Answer 26

ok

Answer 27

sorry my computer is being weird one sec

Answer 28

Another way is to complete the square and convert to vertex form-

-x^2 + 50 x - 264
= -1(x^2 + 50x) - 264
= -1((x - 25)^2 + 625 - 264
= -1(x _ 25)^2 + 361

Answer 29

Sorry im not good at finding the common factors and stuff... so im a little confused

Answer 30

vertex is at (25,361)

Answer 31

ok so -44 and 6

Answer 32

we already found the vertex

Answer 33

yes

Answer 34

rewrite the expression −(x−44)(x−6)
so the x intercets are 44 and 6

Answer 35

yea i know you found vertex already - i was just showing another way of finding it.

Answer 36

ohok lol

Answer 37

Oh ok tha makes since thank yall both (:

Answer 38

so those are the x intercepts 6, 44
in the context of this problem, there is positive profit between selling 6 and 44 memberships. Selling less than 6 memberships and greater than 44 memberships there is negative profit or loss.

Answer 39

@Hannahwaller5 thats what it means

Answer 40

I need to write all this down so i will remeber lol ok thnaks

Answer 41

np