For a function to be continuous at an x-value, say -17, you need to make sure two things line up:
The limit from the left equals the limit from the right.
This limit equals the functions value.
The left hand limit involves the first piece, f(x) = 20x + 1:
The right hand limit invovles the second piece, f(x) = -10x^2:
Since the two one-sided limits don't match, the function is not continuous at x=-17.