# Math Help - standard form

1. ## standard form

I know this is a long question and I have atempted it, although i just really dont have a clue unfortunately

After a few calculations, Allison and Hannah realize the park will make more money if they raise the price of admission. However, they also understand that there must be a limit to how much the park can charge. As a result, they model the situation with the equation, R = (2400 - 80x)(8 + 0.5x), where R represents the revenue from sales and x represents the number of price increases.

1. Write this equation in standard form, R = ax2 + bx + c. Show all of the steps leading to the final answer.
2. What price should the park charge to maximize its revenue?
3. What price range would produce a revenue over \$20,000?

2. 1)
Use FOIL to expand the two binomials. Look here for reference Using FOIL - Free Math Help
You should get $R={-40x^{2}+560x+19200}$

2)
Notice that the function is a parabola opening down. So as $x\to\pm\infty$, $R\to\pm\infty$.
Thus you need to find the vertex to get the highest R value. Use the formula $x={\dfrac{-b}{2a}}={\dfrac{-(560)}{2(-40)}}$.

3)
Set the equation, $=-40x^{2}+560x+19200>20000$ and solve for x.
You should get something like $x < -\left(\sqrt{69}+7\right)$ or $x>\sqrt{69}-7$ as the range.