We can use the vertex form
[tex]y = a {(x - h)}^{2} + k[/tex]
to find the equation of the graph. We know that a is the coefficient, and since the graph opens upwards and is slightly stretched vertically, we know that a is 1/3. On the graph, we see that the vertex of the parabola is at (0,-1). Therefore, h is 0 and k is -1.
Our vertex form equation is
[tex] y = \frac{1}{3} {x}^{2} - 1[/tex]
Which is D
