Final answer:
The parabolic equation provided is in the standard form for parabolas with vertical orientations. The sign of coefficient 'a' determines the opening direction. The positive 'a' in this equation means that the parabola opens upward.
Step-by-step explanation:
In the field of Mathematics, particularly in the context of conic sections, a parabola is a set of all points equidistant from a point (the focus) and a line (the directrix). The orientation or opening of a parabola depends on its equation.
The equation you've provided is in the form (x-h)^2=4a(y-k), where h and k are the coordinates of the vertex and 'a' determines the stretch of the parabola. This is a standard form for a parabola that opens either upward or downward.
If 'a' is positive, the parabola opens upwards. If 'a' is negative, it opens downwards. In this equation (x-3)^(2)=16(y-2), 4a is 16 so 'a' is 4 which is positive, therefore, the parabola does indeed open upward.
Learn more about Parabola Orientation