Problem solving with quadratic functions.

In summary: Why is the equation in the function form?In summary, Homework Statement Eastern Ceramics can sell up to 200 of its flower pots per day in accordance with the demand function.
  • #1
davie08
115
0

Homework Statement


Eastern Ceramics can sell up to 200 of its flower pots per day in accordance with the demand function.

p=13 -.04q

write revenue as a function of the quantity sold q. find the output level q that maximizes R and the selling price at this output level.

Homework Equations


The Attempt at a Solution



okay i tried to put my attempt on here but it was so far from the answer that it would likely confuse you lol.
 
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  • #2
Then why post it here? At least, what did you use for the revenue function?
 
  • #3
okay would you use R=a(q-h)^2 + k
 
  • #4
davie08 said:
okay would you use R=a(q-h)^2 + k

Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV
 
  • #5
Ray Vickson said:
Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV

I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.
 
  • #6
davie08 said:
okay would you use R=a(q-h)^2 + k
What? Where did h, a, and q come from? Thats a general form for a quadratic but you need to use the information from this problem.

davie08 said:
I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.
If you sell 10 items for $5 each, how much money will you receive?

If you sell 50 items for $3 each, how much money will you receive?

How did you calculate that?

Okay, if you sell q items for p each, how much money will you receive?
 
  • #7
davie08 said:
I really have no clue what to use to figure this out can someone just explain what I have to use and then I will understand it and practice it until I'm ready to use it on a test.

We do not do your schoolwork for you here on the PF. You are getting some very good hints, if you would just put forth some effort to try to understand and use the hints.
 
  • #8
Posted from davie08:
okay would you use R=a(q-h)^2 + k

Ray Vickson said:
Why would you think that? If I give you two numbers, one for quantity sold and the other for selling price ($ per unit), how would you compute the revenue?

RGV

He is asking about a form appearing to completing the square as a way to solve, hoping the forum members recognize the standard form.

davie08, completing the square is one possible way to find the maximum, but first give us the complete description of the exercise, word-for-word. What is "p" supposed to be? What is "R" supposed to mean?
 

1. What is a quadratic function?

A quadratic function is a polynomial function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable. It is a type of function that has a degree of 2, meaning the highest exponent in the equation is 2.

2. How do you solve a quadratic function?

To solve a quadratic function, you can use methods such as factoring, completing the square, or the quadratic formula. These methods involve manipulating the equation to isolate the variable, x, and determine its value. You can also use a graphing calculator to find the x-intercepts or roots of the function.

3. What is the difference between solving and graphing a quadratic function?

Solving a quadratic function means finding the value(s) of x that make the function equal to a given y-value. Graphing a quadratic function means plotting points to show the relationship between x and y values, and the shape of the graph can tell you if the function has real or imaginary roots.

4. How can quadratic functions be applied in real life?

Quadratic functions can be used to model real-life situations, such as projectile motion, population growth, and profit maximization. They can help predict outcomes and make informed decisions in fields such as engineering, physics, and business.

5. What are the common mistakes to avoid when solving quadratic functions?

Some common mistakes to avoid when solving quadratic functions include forgetting to distribute negative signs, making calculation errors, and forgetting to check for extraneous solutions. It is also important to be familiar with the properties of quadratic functions and how they can be manipulated to solve for x.

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