Does anyone know the answer to this?

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  B.  y -5 = (1/2)(x +3)^2

Step-by-step explanation:

The parent function f(x) = x^2 has been shifted left 3 and up 5, and scaled vertically. The translation of the vertex to (h, k) can be modeled by ...

  y -k = a(x -h)^2

For (h, k) = (-3, 5), the form of the answer will be ...

  y -5 = a(x +3)^2

Only one answer choice has that form.

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Additional comment

The coefficient 'a' will be positive when the parabola opens upward. This eliminates choices A and C. Choice D represents a translation of 3 units right and 5 units down—directions opposite of those shown on this graph.

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