*Given a function of the form f(x) = ax^2 + bx + c, one can find the zeroes of the function (that is, where f(x) = 0) by using the quadratic formula: x = (-b +- sqrt(b^2-4ac))/(2a).
If the discriminant b^2 - 4ac is less than zero, these roots will be complex or imaginary, and if the discriminant is greater than or equal to 0. these roots will be real.
The use of +- informs us that there are two solutions here; one where we are subtracting sqrt(b^2-4ac), and one where we are adding it.*
For a step by step example, assume the function f(x) = x^2 - 7x + 10. Here a=1, b=-7, c=10. If we set f(x) = 0, then the values of x for which f(x) = 0, that is to say the roots of f(x), would be determined by the quadratic formula: x = (-(-7)+- sqrt((-7)^2 -4(1)(10)))/(2(1)) = (7 +- sqrt(49-40))/2 = (7 +- sqrt 9)/2 = (7+-3)/2. Thus, our roots will be at x = (7+3)/2 and x = (7-3)/2 or x=5 and x=2.
On the graph of the function, we would see that the parabola crosses the x-axis at x=2 and x=5.
