Quadratic function word problem with given equation.

In summary, the profit of a video company, given by P=-5x^2+550x-5000, can be determined by plugging in the amount spent on advertising, x, in thousands of dollars. To achieve a profit of $0, the equation must be set equal to 0 and solved using either the quadratic formula or factoring. The resulting values for x are 10 and 100, meaning that the video company must spend either $10,000 or $100,000 on advertising to make a profit of $0.
  • #1
calcdummy
11
0

Homework Statement


The profit, P, of a video company, in thousands of dollars is given by P=-5x^2+550x-5000, where x is the amount spent on advertising in thousands of dollars.

a) Determine the amount spent on advertising that will result in a profit of $0.


Homework Equations


P=-5x^2+550x-5000


The Attempt at a Solution


P=-5x^2+550x-5000
0=-5x(x-110)-5000
-5x=0 or x-110=0
x=0 or x=110

Therefor when the amount of $110 thousand is spent there will be a profit of $0.

This answer kind of confuses me but on the graph it appears to be accurate. Could someone please review this and tell me if I am incorrect and what I could do to correct it? Thank you in advance.
 
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  • #2
You have the right idea by setting the equation equal to 0! However, what you did is not valid. Try plugging in x=0 and x=110 into the original equation and see what answer you get (it won't be 0).

Since [itex]0=-5x^{2} + 550x - 5000[/itex] is a quadratic function (as you pointed out in the topic title), do you know of any formulas that can solve for x? (were there any you went over in class for this section?)
 
  • #3
scurty said:
You have the right idea by setting the equation equal to 0! However, what you did is not valid. Try plugging in x=0 and x=110 into the original equation and see what answer you get (it won't be 0).

Since [itex]0=-5x^{2} + 550x - 5000[/itex] is a quadratic function (as you pointed out in the topic title), do you know of any formulas that can solve for x? (were there any you went over in class for this section?)


Well I'm home schooled so I'm basically teaching myself all of this. But could I use the quadratic formula to figure out the amount spent to get a profit of zero (x)?
 
  • #4
Ah, okay. But, yes, the quadratic formula is what you can use in this case.

Alternatively, you can factor the equation which is probably the preferred method since using the quadratic formula will give you big numbers. Can you simplify you equation at all to make the numbers smaller to work with?
 
  • #5
I simplified it to -5(x^2-110x+1000) <- is that correct?

with that I tried to use the quadratic formula. Not sure if I was on the right track but I tried anyway... and got:

-(-110)±√-110^2-4(1)(1000)/2(1)

110±√12100-4000/2

110+90/2 or 110-90/2

x=145 or x=65
 
  • #6
calcdummy said:
110+90/2 or 110-90/2

Everything is right up to here. You forgot to divide 110 by 2 also. Remember, you must divide ALL the terms.
 
  • #7
edit - already answered ^
 
  • #8
Hi tal! Thank you for your response. So would that make x=100 & x=10? Also, would my final answer be "In order for the video company to make a profit of $0 they must spend either ten thousand dollars or a hundred thousand dollars in advertisements."?
 
  • #9
Seems right to me.
 

FAQ: Quadratic function word problem with given equation.

1. What is a quadratic function?

A quadratic function is a type of polynomial function with a degree of 2. It can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable.

2. How do I solve a quadratic function word problem?

To solve a quadratic function word problem, you need to first identify the equation that represents the problem. Then, you can use various methods such as factoring, completing the square, or using the quadratic formula to solve for the variable.

3. What information is needed to solve a quadratic function word problem?

To solve a quadratic function word problem, you will need the given equation, the values of the constants a, b, and c, and any other relevant information such as the context of the problem or any additional constraints.

4. What are some real-life applications of quadratic functions?

Quadratic functions have many real-life applications, such as in physics to model the motion of objects, in economics to describe profit and revenue, and in engineering to design bridges, buildings, and other structures.

5. How can I check if my solution to a quadratic function word problem is correct?

You can check the correctness of your solution by plugging the value of the variable back into the original equation and verifying that it satisfies the equation. You can also graph the function and see if the solution matches the point of intersection on the graph.

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