I am a science teacher and I am embarrassed to ask this but, quite honestly, I have found only one website that states it outright.
The focal point of a curved mirror is half the distance from the center of curvature to mirror surface.
Is this correct?
Yes. For a spherical mirror the paraxial focus is located a distance equal to one half the radius of curvature from the vertex. Strictly speaking, this only applies to the “threadlike region around the optical axis” for which sin (theta) = theta holds, but in practice people design optical devices for angles well beyond this ideal region, and they work reasonably well.
If you get too far off-axis, spherical aberration comes into play, and rays parallel to the axis but further from the axis tend to focus closer to the surface that that halfway point, and get closer to the surface the farther from the axis they get. If you want to avoid this, use a parabolic mirror. But spherical surfaces are much easier to generate.
There are plenty of pages devoted to this on the internet. Here’s one, for instance: http://www.kshitij-pmt.com/images-formed-by-spherical-mirrors