# Math Help - Two problems

1. Originally Posted by icemanfan
That's a start. When you multiply it out, you will find that the function is a parabola. Where does the parabola achieve its maximum value?
by changing $-100x^2-6000x+488000$to f(x) = a(x-h)²+k form ?

2. Originally Posted by myaa02
by changing $-100x^2-6000x+488000$to f(x) = a(x-h)²+k form ?
Yes, you want to change the equation to that form. Be careful, though. You made a mistake in multiplying it out. The correct equation is $f(x) = -100x^2 + 2000x + 480000$.

3. Originally Posted by icemanfan
Yes, you want to change the equation to that form. Be careful, though. You made a mistake in multiplying it out. The correct equation is $f(x) = -100x^2 + 2000x + 480000$.
how did you get 2000x if you multiply 100x with 80 ?

nvm i just got it lol

4. what do you do after $-100(x^2-20x+100)+480000-100$ ?

5. Originally Posted by myaa02
what do you do after $-100(x^2-20x+100)+480000-100$ ?
You should get $f(x) = -100(x^2 - 20x + 100) + 480000 + 10000 = -100(x - 10)^2 + 490000$.

Then, observe that the parabola achieves its maximum value at the vertex. What is the vertex of this parabola?

6. Originally Posted by icemanfan
You should get $f(x) = -100(x^2 - 20x + 100) + 480000 + 10000 = -100(x - 10)^2 + 490000$.

Then, observe that the parabola achieves its maximum value at the vertex. What is the vertex of this parabola?
vertex is -10

7. Originally Posted by myaa02
vertex is -10
Incorrect. Remember, the vertex is a point. Also, the x-value of the vertex is not -10.

8. Originally Posted by icemanfan
Incorrect. Remember, the vertex is a point. Also, the x-value of the vertex is not -10.
i seriously don't know how to get the vertex.

9. Originally Posted by myaa02
i seriously don't know how to get the vertex.
If the equation of the parabola is $f(x) = a(x - h)^2 + k$,
then the vertex of the parabola is (h, k).

10. Originally Posted by icemanfan
If the equation of the parabola is $f(x) = a(x - h)^2 + k$,
then the vertex of the parabola is (h, k).
so its (-10,490000)

11. Originally Posted by myaa02
so its (-10,490000)
The vertex is (10, 490000).

12. Originally Posted by icemanfan
The vertex is (10, 490000).
now how am I supposed to find the " new markup " in order to maximize the revenue ?

13. Originally Posted by myaa02
now how am I supposed to find the " new markup " in order to maximize the revenue ?
The function is maximized when x = 10. The markup is 100x, so what should the markup be?

14. Originally Posted by icemanfan
The function is maximized when x = 10. The markup is 100x, so what should the markup be?
So, the markup should be 1000 ?

15. Originally Posted by myaa02
So, the markup should be 1000 ?
Yes, that's correct.

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