Answer: The correct option is (B) below the X-axis.
Step-by-step explanation: We are to select the correct location of the vertex of the following parabola on a co-ordinate grid :
[tex]y=x^2+2x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the standard equation of a parabola with vertex at the point (h, k) is given by
[tex]y=a(x-h)^2+k.[/tex]
From equation (i), we have
[tex]y=x^2+2x-3\\\\\Rightarrow y=x^2+2x+1-4\\\\\Rightarrow y=(x+1)^2-4\\\\\Rightarrow y=\{x-(-1)\}^2+(-4).[/tex]
Comparing the above equation with the standard equation of a parabola, we see that that the co-ordinates of the vertex are (-1, -4).
Since the point (-1, -4) lies in the Quadrant III that is below the X-axis.
Therefore, the vertex of the given parabola lies below the X-axis.
Option (B) is CORRECT.
