The roots of the function are found when y = 0 (that is, the curve crosses the x-axis).
A quadratic may cross the x-axis twice, or it may only touch the x-axis, or it may not cross the x-axis at all. In the first instance, the quadratic will have two roots; in the second instance there will be one root (actually the same root repeated); and in the third instance no real roots (the graph does not cross y = 0).
Crossing the x-axis is the same as solving the equation - the values of x when it crosses the x-axis are the solutions to the equation represented by the garph.
1. Plot the graph for y = x2 - 5x + 6.
|x2 - 5x + 6||42||28||20||12||6||2||0||0||2|
2. What are the roots for y = x2 - 5x + 6?
The roots are given where the line crosses the x-axis, at (2, 0) and (3, 0).
The roots are x = 2 and x = 3.