### Polynomials & Rational Functions

Many ways problem

## Problem

Can you find a cubic curve that…

1. … passes through the $x$-axis at $x=1$ and $x=-1$?

2. … passes through the origin and touches the $x$-axis at $x=-3$?

3. … touches the $x$-axis at $x=2$ and crosses the $y$-axis at $12$?

4. … crosses the $y$-axis at $-6$ and has three integer roots?

5. … crosses the $y$-axis at $y=5$ and touches the $x$-axis at $x=1$?

Are any of the curves described above unique?