# Polynomials

A general polynomial $$p(x)$$ of degree $$n$$ can be written

$p(x)=a_nx^n+a_{n-1}x^{n-1}+ \ldots +a_2x^2+a_1x+a_0$

where $$a_n\neq 0$$. The numbers $$a_n$$ are called coefficients.

A quadratic function is a polynomial of degree two, it has one turning point. Use the applet above to find how many turning points a polynomial of degree five can have. By letting $$a_5=0$$, find how many turning points a polynomial of degree four can have. How many turning points can a polynomial of degree three have?

# Exercises

## Exercise 1 - Quadratic and Line

What conclusion can you make using the applet below. Prove that your observation is always correct.

## Exercise 2 - Cubic and Quadratic

What conclusion can you make using the applet below. Prove that your observation is always correct.