Roots

Roots

GCSE(F), GCSE(H),

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.

Examples

1. Plot the graph for y = x2 - 5x + 6.

Answer: graph showing 2 x squared - 5  x - 6

x-4-3-2-101234
x2 - 5x + 64228201262002

2. What are the roots for y = x2 - 5x + 6?

Answer:

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.