Which of the following could be the equation of the graph above?


[STEP]Write the equation of the parabola having vertex at $(0,-2)$[/STEP]

The vertex of the parabola is $(0,-2)$ and it is an open-upward parabola so the equation is

$$\left(y-(-2)\right) = k(x-0)^2$$

which can be simplified to

$$y=k\cdot x^2-2$$

where $k$ is a constant. The possible equation is the choice $(c)$ which is the equation above with $k=1$.