vertex is (16,3)
slope is 2/2
other points are (18,5) and (14,5)

what's the equation?

"In Cartesian coordinates, a parabola with an axis parallel to the y axis with vertex (h,k), focus (h,k + p), and directrix y = k − p, with p being the distance from the vertex to the focus, has the equation with axis parallel to the y-axis



or, alternatively with axis parallel to the x-axis



You know the vertex, so you know h and k. All you need to know is p and whether the axis is parallel to the x or y axis.

I'm not sure what the slope of a parabola is. I guess it's a rotation of the coordinate system.

You figure out what that means and you can quickly write down the equation. You might have to plug in those two points into one of the equations and see which one gives you the same "p".

Parabola - Wikipedia, the free encyclopedia