Find the Quadratic Equation: Converting Graph with Point (-2,7)

To determine the algebraic representation, we use the vertex form of a parabola, which is $y = (x-h)^2 + k$. Here, the vertex is placed at $(-2, 7)$, thus plug these values into our equation: $h = -2$ and $k = 7$.

Consequently, the equation of the parabola becomes:

$y = (x + 2)^2 + 7$

This representation correctly describes a parabola that passes through the vertex at $(-2, 7)$ and opens upwards, as indicated by the absence of a negative sign or alternate coefficient in front of the square term.

Therefore, the correct choice corresponding to this problem formulation is:

$y = (x + 2)^2 + 7$