What is the connection between the solutions of the equation ax^2 + bx + c = 0 and the x intercepts of the graph of f(x) = ax^2 + bx + c?

Question

The solution says: The solutions of the equation are the first coordinates of the x intercepts.

I did the solutions to the formula but do not understand how these are the first coordinates of the x intercepts.

Thank you.

Answer 1

the intercepts are points with x and y coordinates

for x-intercepts, the y coordinates are zero...but they still exist

Answer 2

Yes, I understand what intercepts are, but I don't understand HOW the solutions to my equation are the first coordinates of my x intercepts.

Am I thinking too much about this?