No. Because apart from its apex, any point on the x-axis is mapped to two points - one above the x axis and one below. A function cannot be a one-to-many mapping.
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It is a square root mapping. This is not a function since it is a one-to-many mapping.
X = Ay2 + By + C
Yes, it is.
Assuming that a is the leading coefficient of the equation of the parabola, changing it from positive to negative will reflect the parabola along a horizontal line through its minimum - which will then become its maximum.
A parabola