Plotting a parabola using Tkinter
Instead of creating an empty list and appending the values to it, try using list comprehension.

so instead of

y_location = []
x_location = []
for each in range(-size, size+1):
    y_location.append(parabola(each, size))
    x_location.append(each)


try

y_location = [parabola(each,size) for each in range(-size,size+1)]
x_location = list(range(-size,size+1))


In general you can use a profiler to see which part of your code requires the largest amount of computing making it easier to improve the code.
https://docs.python.org/2/library/profile.html