Formula 1 - page 2

Enter a polynomial function for the race car's path.
This time you're not given a formula. Instead of dragging points around and watching the formula change, it's up to you to type in the formula that will move the race across the finish line in the fastest time possible!
Question 1
At first, the race car's path is given by the formula[br][br][math]p\left(x\right)=\frac{1}{10}\left(x-2\right)\left(x-10\right)[/math][br][br]What's the degree of this polynomial?
Question 2
Explain why the polynomial[br][br][math]p\left(x\right)=\frac{1}{10}\left(x-2\right)\left(x-10\right)[/math][br][br]won't work. Why do you need a higher degree polynomial?
Question 3
Play around with different polynomials. What's the fastest time in which you can move the race car across the finish line? What's the formula for this polynomial? What are it's roots?

Information: Formula 1 - page 2