Question

The company discovers that it costs $29 to produce 2 widgets, $115 to produce 4 widgets, and $757 to produce 10 widgets. Complete the function that represents the cost, c (x), to produce x widgets. C (x)=?

Answer 1

Looks like this question has been asked before!
questioncove.com/updates/55573d0ee4b0b98f70b37242

Does this help you at all?

Answer 2

I know the steps to the equation. When I did the equation, i got 8x^2-5x, but when I typed my answer in, it said it was wrong, and the correct answer was 8x^2-5x+7. I'm not sure how to get 7 into the equation

Answer 3

Hero should be able to help you out with that, *he is looking at the question, but it may be a little bit before he responds, hence me posting this ¯\_(ツ)_/¯*

Answer 4

Ok, thank you

Answer 5

@Dumbgirl2, I have a solution for this, but I curious, how did you know the function was quadratic?

Answer 6

Because I'm helping my boyfriend with his math, and there is a tutorial you do first, and it tells you at the top what type of function it is

Answer 7

"It tells you at the top what kind of function it is". May I see what it is you're looking at? Can you screenshot it and upload it here if you don't mind?

Answer 8

And easy way to do that would be by hitting the print screen key on your keyboard while looking at it, then simply hitting ctrl+v here while typing a reply, and the image will be auto-uploaded ^_^

Answer 9

Test

Answer 10

Holy wow. That's awesome.

Answer 11

Awesome feature

Answer 12

I figured that would simplify things :P

Answer 13

You should do a tutorial for these cool features.

Answer 14

Perhaps I should. Perhaps I should.

Answer 15

Uhm, It's a wee bit low resolution o-o

Answer 16

Thanks @Dumbgirl2 but I was hoping you could post a screenshot of the actual problem itself.

Answer 17

I already finished the tutorial, but when I started doing practice questions, they made no sense to me, and I even took notes on how to do it, but those don't help. And I can go back and try to get the same one. Sometimes the questions will be different

Answer 18

That's okay, it can be different. I just wanted to observe the structure of the question itself as given from the original source.

Answer 19

Ok, it may be a while until I get question like that again

Answer 20

I'm a very patient person.

Answer 21

Ok, thank you

Answer 22

I see. So it lets you know that you are doing questions on applications of quadratic functions. So that's good because to be honest, I couldn't discern from the question alone what kind of function we're dealing with so that's good.

Answer 23

So the way to go about solving this is to use the fact that a quadratic function, in this case, has the form:
C(x) = ax^2 + bx + c

Now the give you basically three points for (x,C(x)) which are
(2,29), (4, 115) and (10,757)

So you take those points and plug them in to the quadratic function like so:
29 = a(2)^2 + b(2) + c
115 = a(4)^2 + b(4) + c
757 = a(10^2 + b(10) + c

And all that simplifies to:
29 = 4a + 2b + c
115 = 16a + 4b + c
757 = 100a + 10b + c

So what we have is a system of equations in three variables to solve.

Answer 24

To solve for a, b, and c. Solving for that should give you a = 8, b = -5, and c = 7

Answer 25

Hope that answers your question.

Answer 26

How do you get 7

Answer 27

A and B I can usually get, but lately I haven't been getting the answer to C, and I don't know how to get it

Answer 28

Okay, so assuming the values for a and b are correct, we should be able to simply take one of the equations above, input the values for a and b, then solve for c. Let's see what happens:

29 = 4a + 2b + c
29 = 4(8) + 2(-5) + c
29 = 32 - 10 + c
29 = 22 + c
c = 29 - 22
c = 7

Answer 29

Oh my gosh thank you, this all makes sense now

Answer 30

Koolaid

Answer 31

There's another way to get c

Answer 32

Well, basically, it would involve either solving the system fully or converting the system to matrices and solving it that way. But what I've shown above is definitely the easiest way.

Answer 33

And the quickest probably

Answer 34

Well at least the quickest for me

Answer 35

Oh yes, definitely. If you already know a and b, then apply the strategy above, and finding c should be a piece of cake.

Answer 36

It was, thank you

Answer 37

Cool. If you have any other questions, feel free to post them after closing this post. Otherwise, I hope you enjoy the rest of your evening. And good luck helping your friend.

Answer 38

@Dumbgirl2

Answer 39

Do you know how to post this as a new question?

Answer 40

Not unless I go to ask a question and type the question out

Answer 41

Yes you don't have to type the question out completely. Just write New Question

Answer 42

Then post

Answer 43

Ok