Graphing Parabolas that are not parallel to the y-axis

[EuroNerd77]

I have gone over parabolas for a while in my Algebra II class and we are limited to just horizontal and vertical parabolas. I want to figure out how to graph a parabola that is titled at an angle. An equation that let's me graph a parabola whose axis of symmetry is let's say at 43° or 312.45° or whatever degree non parallel to an axis.

 

[mathman]

You can always graph it as a vertical or horizontal parabola and then rotate it so the axis is what you want.

 

[EuroNerd77]

What would you do to the equation in order to rotate it? I need an equation to do this.

 

[SteamKing]

You need to manipulate the coefficients of the general conic equation, as explained in this link:

http://college.cengage.com/mathematics/larson/calculus_early/3e/shared/downloads/clc7eap0e01.pdf

 

[mathman]

What would you do to the equation in order to rotate it? I need an equation to do this.

Essentially you set a matrix with elements (cosx, sinx) for the first row and (-sinx, cosx) for the second row (x is the rotation angle). Each point (x,y) is transformed by mutiplying by the matrix.