If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?

Answer 1

If you mean the zeros of a quadratic of form
ax^2 + bx + c = y
they are where y = 0, or along the x axis.
ax^2 + bx + c = 0
Now there may be two of them because the graph is a parabola.
However if b^2-4ac = 0 then the parabola just hits and bounces off the x axis, never dipping below. That means the two solutions are the same and there is really only one spot where the parabola hits y = 0
Also if b^2-4ac is less than zero, the parabola never hits the x axis but turns and heads back up before it gets there. That means there are no real solutions (There are complex number solutions, but that comes in a later subject.)