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Explanation:
Comparing y = x^2+bx+c to y = ax^2+bx+c, we see that a = 1.
The vertex given is (-2,3). In general, the vertex is (h,k). So h = -2 and k = 3.
Plug those three values into the vertex form below
y = a(x-h)^2 + k
y = 1(x-(-2))^2 + 3
y = (x+2)^2 + 3
Then expand everything out and simplify
y = x^2+4x+4 + 3
y = x^2+4x+7
We see that b = 4 and c = 7.
