At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Well, actually, it seems that you've made at least one mistake in your computation. But the overall approach appears to be correct.
Let's go over it step by step using an example.
Suppose you have \(-y^2\) And \(y = 6\) What value is \(-y^2\) equal to?
Yes. Correct. Now you must ask yourself if your approach here is consistent with what you did above.
There's one way to know for sure if it is correct.
Yes, but you want to know if what you've done is correct, right?
Graph to check: https://www.desmos.com/calculator/kuypcivoou
What do you think it means?
Mind sharing what you think it means?
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.
The first thing you should do is go back and ask yourself what x and f(x) represent.
Exactly, so now in a single sentence, interpret the values of x = 25 and f(x) = 361 in terms of what each represents.
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.
And yes, add "maximum profit" in that sentence as well. You were right with that.
To find the x-intercepts, simply replace f(x) with zero, then solve for x.
I'm sure you can figure this out on your own if you made it that far.
Now you have to ask yourself if both values for x make sense.
If one of them doesn't make sense, you're supposed to discard that value.
Does x = 6 make sense as well?
Remember, the x and y values always come in pairs. In this case we have (x,y) = (6,0)
How much profit was made from the six memberships?
Well, in this case, there is a plausible explanation for the six memberships.
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".
It's a bit of a stretch, but it's a plausible explanation.
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.
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.
Actually, the other point is (44,0) so you must have made a sign mistake somewhere.
ohh ok i see my mistake!
Yes, really. Which basically makes it a bit more difficult to explain why they have no profit after gaining 44 members.
They could have had a raffle and chose 44 people to get a free membership?
No, according to the graph, after 25 members, they start losing profits, so we have to explain in terms of that.
ugh i have no clue >:(
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.
Which causes them to lose the profits they gained. We should assume that the business is a small startup.
Thank you so much for your time!
You're most welcome. Great job on this one.
I cannot help you with anymore questions.