I may have misread that, but it sounds like they want the equation for the parabolic shape which has a focus of 3 cm. If we let axis of symmetry be about the vertical line x=0 and let the directrix be the x-axis, the curvature of the parabolic shape with a focus of f is: y=x^2/(4f), in this case the focus is 3 cm from the x-axis so: y=x^2/12, where x is the distance from the central axis and y is the distance from the x-axis at that point.
A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of the parabolic reflector, 3 centimeters from the vertex. Write an equation that models the parabola formed when a cross section is taken through the reflector’s central axis.