# Sideways Parabola?

Is the only way to get a sideways parabola by the inverse of the function? or can it be translated

### 3 Answers

- Φ² = Φ+1Lv 71 month ago
Parabola with a vertical axis of reflection: y(x) = a(x-h)² + k.

Parabola with a horizontal axis of reflection: x(y) = a(y-k)² + h.

- PopeLv 71 month ago
By sideways parabola do you mean one having a horizontal axis? And by the function do you mean to begin with y equal to a quadratic function in x? If both of those guesses are correct, then no. A quadratic function has no inverse. It is still possible, however, to get that sideways parabola. Simply equate x with a quadratic function in y. Here is the simplest example:

x = y²

Now about that translation: A translation does not change orientation of a figure. The translation image of a parabola will not be sideways unless the original pre-image is.