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Yes, y=2(x−3)2+6 is a function.
When we graph this function, we will get a parabola that opens upwards. The vertex of the parabola is at (3,6) and it is symmetrical. This means that for every x value, there is only one corresponding y value. Hence, it satisfies the vertical line test and is a function.
Here is the graph for better visualization:
*[illustration graph]