Equation of a Tilted Parabola?

[Josiex3]

Hi, I'm trying to find the equation of a tilted parabola. I appreciate your help.

 

[StatusX]

It's not a function. You could write it parametrically by rotating a parametric equation for an ordinary parabola.

 

[tacman]

Sure, I'd be happy to help you find the equation of a tilted parabola. A parabola is a type of quadratic function, which can be written in the form of y = ax^2 + bx + c. However, in order to tilt the parabola, we will need to introduce a new variable, k, which represents the tilt angle.

To find the equation of a tilted parabola, we will use the standard form of a quadratic function, y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, h will represent the horizontal shift of the parabola, while k will represent the vertical shift.

To tilt the parabola, we will use the following formula: x' = xcos(k) - ysin(k) and y' = xsin(k) + ycos(k), where (x', y') represents the new coordinates of the points on the parabola after it has been tilted by an angle of k.

Substituting these new coordinates into the standard form of a quadratic function, we get the equation of a tilted parabola: y' = a(x' - h)^2 + k.

I hope this helps you find the equation of a tilted parabola. Let me know if you have any further questions or need clarification. Good luck!