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Answer:
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.
_____
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.
