Is their such thing as a parabola opening sideways (horizontally)?If so, please explain and give an example.?

Question

The equation of a standard parabola is in standard form : y=ax^2+bx+c, factored form: y=a(x-s)(x-t), and vertex form: a(x-h)^2+k, and the quadratic formula is x = -b ± √(b2 - 4ac)/2a , I'm just curious how it will appear in a horizontal parabola. If their is such thing as a horizontal shaped parabola, please give an example of an equation or a word problem.

Answer 1

Yes. You just have to swap variables, so to speak.

Usually x is the variable and y is the outcome of the function
y=f(x). Here x is the independant variable and y is the dependant variable.

The parabola that we all know and love is y=x^2.
This is the 'vertical' parabola with y as a function of x.

To get a sideways opening 'horizontal' parabola, you would want an equation with x as a function of y.

This new parabola would have equation x = y^2.

Answer 2

Sure, you can have a horizontal parabola.

You can determine which way a parabola opens, vertically or horizontally, by which term is linear and which is squared.

Vertical
y = ax² + bx + c

Horizontal
x = ay² + by + c

You could also have a tilted parabola that is neither vertical nor horizontal. But you would have to introduce an xy term for that.