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?