Parameter of a quadratic from a line meeting it once, its factorised and completed square forms and where it is negative and increasing

The function \(f\) is defined by \(f(x)=mx^2+6mx\) for \(x\in\mathbb{R}\), where \(m\in\mathbb{R}\). The graph of \(f\) and the line \(y=2mx-8\) have exactly one point in common.

1. Show that \(m=2\).[6]

With this value of \(m\), \(f(x)\) can also be written as \(2(x-p)(x-q)\), where \(p\) and \(q\) are real constants.

2. Find \(p\) and \(q\).[2]

In completed-square form, \(f(x)=2(x-h)^2+k\), where \(h\) and \(k\) are real constants.

3. Find \(h\) and \(k\).[3]
4. Hence, find the interval of values of \(x\) for which \(f(x)<0\) and \(f\) is increasing.[3]