Given critical points, find the original function of two variables

Question

I am unsure how to attempt this question as it entails two variables.

Find a function $f:ℝ^2→ℝ$ that has local extrema at $f(x,y)$ for all $[x,y]∈P$

$$P={\{[-8,5],[-7,6],[-5,2],[-3,-4],[5,5]}\}$$

N.B. The local extrema in your function must pass the 2-variable 2nd derivative test.