Final answer:
The function represents a vertical stretch by a factor of 4 and a vertical translation up 10 units, but it does not include a reflection over the y-axis.
Step-by-step explanation:
The given function is f(x) = -4(-2)^2 + 10, which is a quadratic function. We're looking at the possible transformations this function could represent. When we analyze the function, we notice that the negative coefficient in front of the squared term does not reflect the graph across the y-axis, as that would require x to have a negative exponent. Instead, it creates an upside-down parabola, which is a vertical reflection. Therefore, reflection over the y axis is not a transformation represented by this function. It does, however, have a vertical stretch by a factor of -4, it is translated up by 10 units, but it does not involve any horizontal translation, so it neither moves left nor right.