# 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 79 months 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.

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- PopeLv 79 months 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.

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- 9 months ago
The only way to get a sideways parabola is to have some form of x = y^2

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