How to connect 8 vertices to 3 with all quads? These are the vertices I'm trying to connect

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And this is my best attempt at doing so without distorting the mesh too much

I still ended up with a triangle, and some awful geometry that made smoothing out the mesh a lot harder. Am I doing anything wrong? Is there a better way to do this?
I considered adding more edge loops on the left side, but I have subdivision surface modifier on, and adding more edge loops there sharpens the mesh too much.

Question
How do I fill in the hole while avoiding n-gons?
Your situation has an even amount of vertices.
They cannot be connected with only quads.
Each inserted quad will always add/subtract exactly 2 vertices to/from a hole and you will always end up with 3 vertices in the end.
After adding one more vert you can easily achieve quads for example like this: