Given the function y = - x ^ 2 + | x + 2, seek the image, seek the monotone interval, seek the maximum value of the function

Given the function y = - x ^ 2 + | x + 2, seek the image, seek the monotone interval, seek the maximum value of the function

First of all, we can prove that f (x) is an even function, which is symmetric about the y-axis
F (0) = 2, i.e. passing through (0,2) point
f(x)