Problem 123

Let D be the projection of point M on the directrix. According to the definition of a parabola, we know that |MF|=|MD|.

To find the minimum value of |MP|+|MF|, we need to find the minimum value of |MP|+|MD|. This occurs when points D, M, and P are collinear, with a minimum value of 2-(−2)=4.

Therefore, the answer is $\boxed{4}$.

By setting point D as the projection of M on the directrix, we can transform the problem into finding the minimum value of |MP|+|MD|. We can then deduce that the minimum value occurs when points D, M, and P are collinear, providing us with the answer.

This problem tests your understanding of the definition and standard equation of a parabola, as well as the application of its simple properties. Recognizing that |PM|+|MD| is minimum when points D, M, and P are collinear is the key to solving this problem.