help

If it is a square centered on the origin....     then   |x| = |y|.  At the corner that intercepts the parabola.....compute the formula of the parabola first.....then......

The graph touches the x-axis at only 1 point. This means the equation of the graph must be a product of a perfect square and a real constant, in this case:

$y = k(x + 1)^2$

When x = 0, y = 2.

$2=k\cdot 1^2\\ k = 2$

Therefore, the equation of the parabola is $y = 2(x + 1)^2$.

If it is a square with one of the vertices being the origin, then two of the vertices lies on |y| = |x|, in this case, two of the vertices lies on y = -x.

We solve the system of simultaneous equations

$\begin{cases}y = 2(x + 1)^2\\y = -x\end{cases}$

I will leave the rest for you.