A quadratic has an axis of symmetry of x=m, and the quadratic hax an x-intercept at (m,0). The quadratic has a vertical compression as a approaches infinty y approaches negative infiniy. What is a possible equation of the quadratic?

The quadratic has an x-intercept at (w,0).
Its axis of symmetry is x=w,so it can be taken as ${\displaystyle y=k{(x-w)}^2}$ where k is constant.
From given information the quadratic has a vertical stretch and as x approaches ${\displaystyle \mathrm{\infty }}$ and y approaches ${\displaystyle -\mathrm{\infty }}$ so must have,k<0
So let us take k=−2.
Hence the possible equation of the quadratic becomes,${\displaystyle y=-2{(x-w)}^2}$