Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?

In vertex form, g(x) = a(x − h)² + k, the graph shifts right by h and up or down by k. A positive a means the parabola opens upward, so it has a minimum. Choice D, g(x) = 8(x − 3)² − 5, shifts right 3 and down 5, and its positive coefficient gives it a minimum.

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