Do I need to update stored Azure Function URL if I pass a new parameter?

We have an Azure Function with an HttpTrigger written in Python for which a team now needs a parameter sent in for a POST request (I suggested header, but it was written to grab the parameters).

We have a key for the Azure Function, so the URL is likehttps://fa-url.azurewebsites.net/api/fa-name?code=ms-code-for-fa.

We call this Azure Function from a C# project after grabbing the Function's URL from Azure. If I now update the URL to accept a parameter, say param1, do I need to update the function URL stored in Azure to be something like https://fa-url.azurewebsites.net/api/fa-name?code=ms-code-for-fa&param1=value?

Or can I keep our stored URL the same and call that URL but tack on the query parameter by concatenating original URL + query parameter in C#? I feel like this would return 404, but I'm missing something obvious here.