Find Tilted Parabola Equation given vertex and angle

How to find the parabola equation like the picture below, given the vertex $(x$$_o,y_o)$ and theta orientation? please help. thankyou.

Using some trigonometry:

Let $ y = a(x-h)^2 + k $ represent the equation of the parabola at vertex $(h, k)$ on the $xy$ plane

A two dimensional rotation is described as $$x = x'\cos(\theta) + y'\sin(\theta)$$ $$y = -x'\sin(\theta) + y'\cos(\theta)$$ where $(x', y')$ is a point on the $x'y'$plane rotated by $\theta$

Substituting these formulas into the equation of the parabola we get

$$-x'\sin\theta+y'\cos(\theta)=a(x'\cos(\theta) + y'\sin(\theta) - h)^2+k$$

which is probably the most useful form as simplifying gets messy

Here is a desmos link with a rotating parabola: https://www.desmos.com/calculator/hguanwbkbu