1. ## Quadratic function word problems

Hey guys, I have a word problem I'm confused/ stuck on.

A video game company is selling a new console, the sales of the the system will follow the quadratic function y = -1/50x^2+7x-200.

1. After how many days is the company going to make a profit?

2. After how many days do they reach their peak sales?

3. How many days can they expect to be making a profit on this product?

4. What is a reasonable domain and range for this?

So I started out with -b/2a. I got 175 and plugged it into the equation and ended up with 412.5.
I'm confused because I don't know if I found the answer to # 1 or # 2. I'm guessing I got the maximum for # 2, but what would I find for number 1?

And the rest I have no clue on what to do.

Sorry if this sounds confusing.

2. For number one, i suggest setting the equation equal to zero, and then solving using the quadratic formula. You know that since 0 is no profit, the value that equals zero is when they will have no money. So they will make money at whatever value is greater than the answer you solved for. And you are right, 412.5 is the maximum profit, and if x is in days, this is made after 175 days.

3. Thank you so much! But I find both # 1 and # 3 to be asking the same thing? Can you explain to me what those two are asking?

4. Number 1 asks how long it will take the company to make a profit.

Number 3 asks how long the company will CONTINUE to make a profit.

5. Originally Posted by Jubbly
Thank you so much! But I find both # 1 and # 3 to be asking the same thing? Can you explain to me what those two are asking?
Number 3 is asking the length of time it will remain in profit whereas 1 asks how long it takes to get an initial profit.

This will be the period between the two solutions given by the quadratic formula

6. The graph of this quadratic function is a parabola with vertex upward. There will be a time, from 0 to $t_0$ days, say, while the graph is below the axis, then a time, from $t_0$ to $t_1$, say, when it is above the axis, then it goes back down.

"1) After how many days is the company going to make a profit?"
is answered by $t_0$, the time from t= 0 until the graph is above the axis.

"3) How many days can they expect to be making a profit on this product?"
is answered by $t_1- t_0$, the time in days that the graph is above the axis.

"So I started out with -b/2a. I got 175 and plugged it into the equation and ended up with 412.5. "
Can you say why you did those things? There is no point in using a formula if you don't know what the formula is for!