Since this is a quadratic function, we will be using a polynomial with a degree of 2.
The parent function of the quadratic function is x^2. Using this function for refrence, we see that there are some changed.
First, the function was shifted 2 units to the left, so we rewrite this as (x+2)^2, we also see that the function was also shifted 5 units up so we write, ((x+2)^2)+5, and finally, we see the function was flipped vertically, so we make this a negative,
(-(x+2)^2)+5.
Now, let's confirm this is the answer by plugging in the given coordinates!
5 = (-((-2)+2)^2)+5, ((0)^2)+5, 5.
1 = (-((-4)+2)^2)+5, ((-2)^2)+5, -4+5, 1.