Find the largest and smallest value of the function y = 2x ^ 2 on the segment [-2; 2].

1. The graph of the function y = 2x ^ 2 is a parabola with apex at the center of coordinates and with branches pointing up.

2. Consequently, the smallest value of the function on a given interval [-2; 2] will be at the point x = 0:

y (min) = y (0) = 0,

and the largest value is at the ends of this segment:

y (max) = y (-2) = y (2) = 2 * 2 ^ 2 = 2 * 4 = 8.

Answer. The smallest and largest values of the function on the segment [-2; 2]: 0 and 8.