if you draw the two inequalities, you will see clearly where the corners are. you have to find the bounded area and then look for any intersections around it. to find any intersecting lines, first convert the inequalities to equal signs (=), then solve for y for both

y = x^2

y = 12 - 2x^2

then make them equal and solve for x

x^2 = 12 - 2x^2

here is a picture of the corners

View attachment 39568