Searching for a function with one parameter like in the example

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I am searching for a math function with one paramter a which is doing the weighting like in the picture. For a=0 the function is linear (y=x) and for the maximum a=1 the weighting is high for P_2 and low for P_1 (inverse for the minimum a=-1). Which function is it?

https://i.stack.imgur.com/wm0zL.png