QuadRatic Function Word Problem (The use of drinking water in a factory)

[IAmNich]

Hello all, I am new to this site and have never posted before but I come in a dire request for help on a word problem.

The Word Problem is as follows:

The use of drinking water in a factory varies as a function of the time of day. This Situation can be modelled by a second degree polynomial function. The amount of water used reaches a maximum of 200 L at 13:00, while there is no water used at 7:00 and 19:00.

A) What is the general equation associated with the use of water?
B) At what time does the factory need 150 L of water?


Thank you for your help on this question in advance.

 

[Deleted member 4993]

Hello all, I am new here and I come looking for help on a quadratic function word problem.

The problem is as follows:

The use of drinking water in a factory varies as a function and the time of day. This situation can be modelled by a second degree polynomial function. The amount of water used reaches a maximum of 200 L at 13;00, while there is not water used at 7;00 and 19;00.

A) What is the general equation associated with the use of water?
B) At what time does the factory need 150 L of water?

Thanks in advance.

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for

 

[Dr.Peterson]

The use of drinking water in a factory varies as a function of the time of day. This Situation can be modelled by a second degree polynomial function. The amount of water used reaches a maximum of 200 L at 13:00, while there is no water used at 7:00 and 19:00.

A) What is the general equation associated with the use of water?
B) At what time does the factory need 150 L of water?

The problem as stated doesn't quite make sense; you must not have copied it correctly.

At any particular moment in time, a factory will not use any water. It might be using 200 liters per hour, or per minute; but it can't use 200 liters of water all exactly at 13:00!

(Or maybe it has used 200 liters of water from midnight until 13:00; no, that can't be what it means, because it would have had to return water to the city between then and 19:00 in order for the total used to go down to zero.)

So the units are wrong. If we just suppose it's really L/hr, then the claim is that the rate of usage, R, is a quadratic function such that R(13) = 200, which is the maximum, R(7) = 0, and R(19) = 0.

What have you learned that might be useful to find this function? As you've been reminded, this site wants to help you solve a problem, which means you have to tell us what help you need, showing us whatever you have been able to do. We don't just do it for you.

Now, there is actually more information here than you need, so you could use any of several different approaches; that's another reason we need to know whether you have learned about the vertex, or factored form, or whatever.

Another thing missing from the problem is the domain. This function can't apply to all times of day; can you see why?

 

[IAmNich]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for

So what I don't understand is how to start the problem, I know that I must find the rule before doing anything. But I don't know how to find the rule. So I suppose that I need help with finding the rule. I'm pretty sure I can finish the problem once I have established the rule.

 

[IAmNich]

The problem as stated doesn't quite make sense; you must not have copied it correctly.

At any particular moment in time, a factory will not use any water. It might be using 200 liters per hour, or per minute; but it can't use 200 liters of water all exactly at 13:00!

(Or maybe it has used 200 liters of water from midnight until 13:00; no, that can't be what it means, because it would have had to return water to the city between then and 19:00 in order for the total used to go down to zero.)

So the units are wrong. If we just suppose it's really L/hr, then the claim is that the rate of usage, R, is a quadratic function such that R(13) = 200, which is the maximum, R(7) = 0, and R(19) = 0.

What have you learned that might be useful to find this function? As you've been reminded, this site wants to help you solve a problem, which means you have to tell us what help you need, showing us whatever you have been able to do. We don't just do it for you.

Now, there is actually more information here than you need, so you could use any of several different approaches; that's another reason we need to know whether you have learned about the vertex, or factored form, or whatever.

Another thing missing from the problem is the domain. This function can't apply to all times of day; can you see why?

I can assure you that I have indeed copied down the question correctly. As you can see the wording confuses me and therefore causes me to get stuck. As question A) suggests I believe that the rule must be written in the general form of the quadratic equation. I have learned about the 3 forms of the quadratic equation being: Factored, General and Transformed (Standard). I have all learned the different parameters of the forms, example: vertex, parameter a and etc...

 

[Dr.Peterson]

I can assure you that I have indeed copied down the question correctly. As you can see the wording confuses me and therefore causes me to get stuck. As question A) suggests I believe that the rule must be written in the general form of the quadratic equation. I have learned about the 3 forms of the quadratic equation being: Factored, General and Transformed (Standard). I have all learned the different parameters of the forms, example: vertex, parameter a and etc...

Ok, let's just focus on the main ideas; they just made a mistake with units. I boiled it down for you to take away the confusion of words:

The claim is that the rate of usage, R, is a quadratic function such that R(13) = 200, which is the maximum, R(7) = 0, and R(19) = 0.
​

The maximum is the vertex, right? And you've learned about that. So you have a parabola whose vertex is at (13, 200), that also passes through (7, 0) and (19, 0). Do you know how to find an equation for that?

Or, you have the two zeros, 7 and 19, and another point, (13, 200). Can you use factored form to write an equation for that?

Then, either way, rewrite the equation in general form.