Is there a way to plug this equation into a graphing calculator?

No

Vivian, even though you can't use a graphing calculator, this is a good one to use plugging in and elimination. Plugging in 0 as Y in the equations, we are looking for x= -1

We can eliminate B, because here x= - 0^2 = 0
We can also eliminate C, because here x= -0 + 1 = 1
We can eliminate E, because here x= (0+1)^2 = 1

We are left with A and D. How do we choose between them?
In the graph, the values of x are all negative and lower than -1.
- When we look at equation D, x will have some positive values, i.e.,, when y=2 or y=3 etc. In fact the graph for D is a sideways parabola bottoming out at -1
When we look at equation A, the x values are all negative, consistent with the graph. Try plugging in 1, 2, for example.

Hence the answer is A.

The produced solution is wrong, the answer is certainly C. Since the graph is moved LEFT, you have to make it (x+1)= -y^2 which is equivalent to x=-y^2 - 1

Btw A is incorrect because the graph of A includes a y-intercept at (0,-1) and for multiple other reasons but this one is most evident because you can clearly see it...

A square is ALWAYS positive, so if the function were x=y^2, the line would be tangent to the y-axis and reflected on the positive x-axis. But in this case the function is negative, so we can eliminate the last two choices.

I got it