This Instructable will use FreeCAD's v0.17 new tool for drawing parables in sketches.
There are ways to do this with older versions, but are far more troublesome than the way I show here.
Step 1: Install and Run FreeCAD 0.17
Download and install FreeCAD 0.17 following the instructions in this link: https://www.freecadweb.org/wiki/Release_notes_0.17...
Once v0.17 is installed, open it and click "create a new empty document."
Step 2: Create a New Sketch
Select the "Sketcher" toolset from the drop down menu and click the "create new sketch" button. FreeCAD will then prompt for the sketch plane orientation. I chose XY for this drawing.
Step 3: Select the "Arc of Parabola Tool"
Select the "Arc of parabola by focus, vertex and endpoints" from the conic curves drop down button and click it.
Step 4: Select Your Focus Point, the Vertex and the Endpoints Coordinates
First click will set the focus coordinates, second click will set the vertex and the last two clicks the two endpoints (you can change the coordinates of all of the points later.)
Step 5: Set the Distante From the Focus to the Vertex Points
Using the horizontal distance tool, set the distance from the focus point to the vertex of the parabola. In this case I want the focus point to be at 20cm from the vertex.
Similarly, using the vertical distance tool, I set the vertical distance from the vertex to the endpoint at 150mm for a 300mm dish. If this were a solar reflector, it would concentrate a power of about 75W at a ratiation level of 1000W/m2.
Step 6: Adjust the Other Endpoint and Fully Close the Sketch Drawing
Set the other endpoint on the horizontal axis and then, using horizontal and vertical lines, close the drawing.
In a later step, I will perform a revolution to create a solid, so I only draw a half of the parabola. If it's not a closed figure FreeCAD will complain with error messages.
Leave the sketching mode by pressing escape or clicking the close button on the left panel.
Select the recently created sketch and then click the "Revolve" tool from the "Part design" menu. FreeCAD will complain with an error, reporting that first a "body" must be created. Select the sketch in the left panel and click the "Create a new body and make it active" button from the "Part design" menu. Then try the revolve tool again.
In the left panel check the "From different parts or free features" option and then click the sketch in the area just above the options. Then click the "OK" button.
In "Revolution parameters" select "Horizontal sketch axis" and then the "OK" button again.
Step 9: Now You Have a Reversed Paraboloid
Of course, you could have designed a concave solid in the sketch by closing it backwards, but I find this way useful to "carve" paraboloids in arbitrary solids and at any angle.
Step 10: Now Use the Convex Paraboloid to Cut From Other Solids
In this example I'm cutting from a solid block to obtain the result I was looking for. Then I can shape the resulting solid to fit the requirements of the design, the size of the printer and many other factors.