Extract Vertex from LaTeX Input

Hi, I’m making an activity on vertex form of quadratic functions, and I was wondering if there’s a way to extract the vertex from a LaTeX string in vertex form. I’ve created this sample to show what I’m trying to do. If you put in the correct equation, it works how I want it to work, but you’ll see the problem if you put in an incorrect function.

I suspect patterns might do it, but that might be making it overly complicated.

Some calculus gets you there. Looked at patterns, but yeah complex.

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Brilliant! That’ll work great. Thank you so much!