Reading the graph

In this question, I found that the roots of the quadratic are -1/2 and 1 when the quadratic equals 0.

Just wanted clarity on this:

If the constraint x > -1/2 was not given to us, then by graphing the parabola for the quadratic, we could see that for x values lesser than -1/2 and greater than 1, the y values are greater than 0.

Therefore the answer would be D right?

Please correct me if I’m interpreting the graph wrong.

Yes