Question 991228
Try like this:
{{{y=ax^2}}} for vertex at the origin.  A point on the parabola reflector is  (1,1/4) using your second part of the description.  That is 1 inch on each "side" in the cross section at the bulb.  That makes the two inch cross section.


{{{1/4=a*1^2}}}
{{{a=1/4}}}
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{{{y=(1/4)x^2}}}, but this may not match the first part of the description for the bulb at the focus, {{{1/4}}} inch from the vertex.  Recheck your problem description to be sure.