Here's a graph of two such parabolas.
Since they cross the y-axis at 0, then c=0.
P(-2,0) and Q(0, 0)
Plug in the coefficients into the equation:
and therefore the equation of parabola1 becomes:
Do just the same to calculate the equation of parabola2. You should come out with
The domain is [-2, 0] or [0, 2] respectively.
By the way: You can get one function whose graph is the required "M":
The height of the letter is the y-coordinate of the vertex of one parabola. I don't know which method you prefer to calculate the vertex but you should get:
To answer #5 I've sketched a family of curves:
for a running from 2 to 6 in steps of 0.5. Now make your choice!