(a) Intercepts: When y=0, (x^2-x)^2=x^2; x^2-x=+x. So we have x^2-x-x=0 or x^2-x+x=0. x(x-2)=0 or x^2=0. So x=0 or 2; when x=0, y^4=y^2 and y^2(y-1)(y+1)=0, so y=0, 1 or -1. Therefore we have intercepts at (0,0), (0,1), (0,-1) and (2,0). That is, three on the y axis and 2 on the x axis (the origin is an intercept for x and y). The origin is the cusp of the cardioid and the body of the cardioid cuts the x axis at x=2.
(b) If we put -y into the equation we get the same results for x as we do when we put +y into the equation. So the graph is symmetrical about the x axis. If we put -x into the equation, the contents of the brackets becomes (x^2+y^2+x), which is not equal to (x^2+y^2-x) when we have +x. So even though this expression is squared, it's the square of a different number. So the graph is not symmetrical about the y axis. To check this out, put x=1 in the equation: y^4=y^2+1, y^4-y^2-1=0, so y^2=(1+sqrt(5))/2 and y is plus or minus the right hand side (above and below the x axis); now put x=-1: (y^2+2)^2=y^2+1; y^4+3y^2+3=0, which has no real roots, so the graph curve doesn't exist at x=-1, which is to the left of the origin.