How do i solve this optmization problem?

You are trying to minimize the distance to (1--1); it might be easier if we minimize the square of the distance so we don't have square roots. (x-1)^2 +(y+1)^2 =d^2. y=x^2-1 so add one and you get y=x^2.which squares as x^4, so (x^2-2x+1)+x^4 =d^2; now take the derivative of the left and set to 0; 2x-2 +4x^3=0. You may need a calculator or a graphing utility to find the root. that is your x, then to find the y take that squared and subtract 1 (since y=x^2-1).