The given equation is \( y = (x+7)^2 + 3 \).
This is a quadratic function in the form \( y = a(x-h)^2 + k \), where \( (h, k) \) represents the vertex of the parabola. Here, \( a = 1 \) (which is positive), so the parabola opens upwards.
From the equation, we can identify:
- \( h = -7 \)
- \( k = 3 \)
The vertex \( (-7, 3) \) is the minimum point of the graph. Thus, the minimum value of \( y \) occurs at \( y = 3 \).
So, the minimum of the graph is \( 3 \).
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