How are the real solutions of a quadratic equation related to the graph of the quadratic function?

2 answers

They are the points where the graph crosses the x-axis. That is, where

ax^2+bx+c = 0
the solutions to the quadratic equation correspond with the x-intercepts of the corresponding function

e.g.
the solutions of
x^2 - 7x + 12 = 0
are x = 4 or x = 3

and the graph of y = x^2 - 7x + 12 has x-intercepts of 3 and 4