Its seriously fun to have kids who come home from school with algebra assignments to make things like this. On a clear day it will ignite a newspaper in 4 seconds and boil a cup of water dry in 4 minutes.
Here you go: Ax² + By² + Cx + Dy + E = 0 (if you really need to know what that means I'll have to ask my kids) Once you determine the y you want to use you graft it life size.
We started by turning a very shallow but thick bowl (8" diameter X 4" thick with less than 1/2' bowl indention) and cutting 16 notches in it around the edges; it looks like a big gear. Then we used the life sized graph cut out to cut 16 ribs out of thin plywood; the ribs are about 30 inches long and they curve up 12 inches, each rib plus the radius of the hub combine to the radius of the parabols, about 33" in this case. The bowl is covered with thin sheet aluminum and it is covered with mylar.
look up tracking solar concentrator on google. There are plans out there. Makes one hell of a water heater! It was a green solution developed back when being green wasn't cool like it is today.
I had made one about 6 feet across when I was in school. I cut a couple thousand mirror sections and glued them to a steel sheetmetal frame. It worked well and would melt lead.