The equation of parabola is . If a is positive and is always greater than zero or equal to zero, then x is also greater or equal to zero. This means that parabola is determined for non-negative x and for all real y.
Tha canonical equation of parabola is , where p>0. The branches of this parabola go up in positive y-direction. When you change x to y and y to x, then the branches of parabola go in positive x-direction, that is right.
