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The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
This is called the 'standard form' for the equation of a parabola:y =a (x-h)2+vDepending on whether the constant a is positive or negative, the parabola will open up or down.
If the value of the variable is negative then the parabola opens downwards and when the value of variable is positive the parabola opens upward.
I think it's like this: x2+3x-5 So if the x2 part is a positive then it opens upward but if it's negative it goes downward.
It is a square root mapping. This is not a function since it is a one-to-many mapping.