Polynomials are some of our favorite functions.
What are polynomial functions?
The phrase above ‘‘in the variable ’’ can actually change. is a polynomial in , and is a polynomial in .
What can the graphs look like?
Fun fact:
Remember, a root is where a polynomial is zero. The theorem above is a deep fact of mathematics. The great mathematician Gauss proved the theorem in 1799 for his doctoral thesis.
The upshot as far as we are concerned is that when we plot a polynomial of degree , its graph will cross the -axis at most times.
- Curve is defined by an evenodd degree polynomial with a positivenegative leading term.
- Curve is defined by an evenodd degree polynomial with a positivenegative leading term.
- Curve is defined by an evenodd degree polynomial with a positivenegative leading term.
- Curve is defined by an evenodd degree polynomial with a positivenegative leading term.