The equation given is \( y = (x + 7)^2 + 3 \). This is in the form of a quadratic function, specifically \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
In this case, we have:
- \( a = 1 \) (which is positive, indicating the parabola opens upwards)
- \( h = -7 \)
- \( k = 3 \)
The vertex of the parabola occurs at \( (h, k) = (-7, 3) \).
Since the parabola opens upwards, the vertex represents the minimum point on the graph.
Thus, the minimum value of \( y \) is:
\[ \text{Minimum} = k = 3 \]
Therefore, the minimum of the graph described by the equation \( y = (x + 7)^2 + 3 \) is 3.