Question

HI

Answer 1

Well, actually, it seems that you've made at least one mistake in your computation. But the overall approach appears to be correct.

Answer 2

Let's go over it step by step using an example.

Answer 3

Suppose you have

\(-y^2\)

And \(y = 6\)

What value is \(-y^2\) equal to?

Answer 4

Yes. Correct. Now you must ask yourself if your approach here is consistent with what you did above.

Answer 5

There's one way to know for sure if it is correct.

Answer 6

Yes, but you want to know if what you've done is correct, right?

Answer 7

Graph to check: https://www.desmos.com/calculator/kuypcivoou

Answer 8

What do you think it means?

Answer 9

Mind sharing what you think it means?

Answer 10

Actually (x,y) = (25, 361)

What the question wants us to do is describe the relationship between the x and y values for the vertex in terms of what is stated in the problem.

Answer 11

The first thing you should do is go back and ask yourself what x and f(x) represent.

Answer 12

Exactly, so now in a single sentence, interpret the values of x = 25 and f(x) = 361 in terms of what each represents.

Answer 13

You're on the right track, but do it in a way that shows the relationship. Say it this way:

The yoga studio made $361 in profit for the 25 members it processed in its current month.

Answer 14

And yes, add "maximum profit" in that sentence as well. You were right with that.

Answer 15

To find the x-intercepts, simply replace f(x) with zero, then solve for x.

Answer 16

I'm sure you can figure this out on your own if you made it that far.

Answer 17

Looks right.

Answer 18

Now you have to ask yourself if both values for x make sense.

Answer 19

If one of them doesn't make sense, you're supposed to discard that value.

Answer 20

Does x = 6 make sense as well?

Answer 21

Explain

Answer 22

Remember, the x and y values always come in pairs. In this case we have
(x,y) = (6,0)

Answer 23

How much profit was made from the six memberships?

Answer 24

Well, in this case, there is a plausible explanation for the six memberships.

Answer 25

If we assume that this is the first month of operation for the yoga studio since its grand opening, as part of its advertisement, the yoga studio could have stated something like, "The first six customers get a free membership".

Answer 26

It's a bit of a stretch, but it's a plausible explanation.

Answer 27

The other plausible explanation is that the first six members represent the original team who put the business together in the first place so of course they don't make any money off themselves.

Answer 28

The question says to explain each value in the context of the problem. We already know there's no such thing as negative members. That is impossible. However, for x = 6, for this particular problem we can't make sense of it either unless we come up with plausible explanations such as what I posted above. That's all you can do for this question.

Answer 29

Actually, the other point is (44,0) so you must have made a sign mistake somewhere.

Answer 30

https://www.desmos.com/calculator/mebdvn94g7

Answer 31

really?

Answer 32

ohh ok i see my mistake!

Answer 33

Yes, really. Which basically makes it a bit more difficult to explain why they have no profit after gaining 44 members.

Answer 34

oh gosh

Answer 35

They could have had a raffle and chose 44 people to get a free membership?

Answer 36

No, according to the graph, after 25 members, they start losing profits, so we have to explain in terms of that.

Answer 37

ugh i have no clue >:(

Answer 38

The plausible explanation is that the studio can support up to 25 members at a time. If they have more than 25 members, then they have to rent more building space, purchase more equipment, etc.

Answer 39

Which causes them to lose the profits they gained. We should assume that the business is a small startup.

Answer 40

oh ok

Answer 41

Thank you so much for your time!

Answer 42

You're most welcome. Great job on this one.

Answer 43

I cannot help you with anymore questions.