Question

Where is the location of the vertex of the parabola on a coordinate grid?

y=x^2+2x-3

A. above the x-axis
B. below the x-axis
C. on the x-axis
D. on the y-axis

Answer 1

D. on the y-axis is the answer

Answer 2

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 :

`y=x^2+2x-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

the standard equation of a parabola with vertex at the point (h, k) is given by

`y=a(x-h)^2+k.`

From equation (i), we have

`y=x^2+2x-3\\\\\Rightarrow y=x^2+2x+1-4\\\\\Rightarrow y=(x+1)^2-4\\\\\Rightarrow y=\{x-(-1)\}^2+(-4).`

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.