Answer:
D. y=(x+1)^2
I’m assuming that the parenthesis at the end is there because of vertex form (It would not make sense otherwise)
Step-by-step explanation:
The vertex form is y=a(x-h)^2+k with (h,k) being the vertex. The vertex(midpoint of the parabola) in the graph is (-1, 0). Assuming from the possible answers, the a is 1 throughout because none of them have a constant by x. Therefore, when plugging in the vertex to the vertex form, the answer is y=(x+1)^2 or in standard form (ax^2+bx+c), y=x^2+2x+1.
Another method to solve this could be plugging in points to see if they fit. Though this takes longer, it works. For example, take (-2, 1) from the graph. Plug in the x value for all the equations to see if you get 1. For equation A, you get y=5. For equation B, you get y=3. For equation C, you get y=9. For equation D, you get y=1. Because D is the only equation that had the point that aligned with the graph, D is the correct answer. I would much rather the first method if possible due to it’s quicker efficiency though.