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 $20,000? 2. 1) Use FOIL to expand the two binomials. Look here for reference Using FOIL - Free Math Help You should get$\displaystyle R={-40x^{2}+560x+19200}$2) Notice that the function is a parabola opening down. So as$\displaystyle x\to\pm\infty$,$\displaystyle R\to\pm\infty$. Thus you need to find the vertex to get the highest R value. Use the formula$\displaystyle x={\dfrac{-b}{2a}}={\dfrac{-(560)}{2(-40)}}$. 3) Set the equation,$\displaystyle =-40x^{2}+560x+19200>20000$and solve for x. You should get something like$\displaystyle x < -\left(\sqrt{69}+7\right)$or$\displaystyle x>\sqrt{69}-7\$ as the range.