Can you find a cubic curve that…
… passes through the \(x\)-axis at \(x=1\) and \(x=-1\)?
… passes through the origin and touches the \(x\)-axis at \(x=-3\)?
… touches the \(x\)-axis at \(x=2\) and crosses the \(y\)-axis at \(12\)?
… crosses the \(y\)-axis at \(-6\) and has three integer roots?
… crosses the \(y\)-axis at \(y=5\) and touches the \(x\)-axis at \(x=1\)?
Are any of the curves described above unique?
