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.

1. Plot the graph for *y* = *x*^{2} - 5*x* + 6.

Answer:

x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |

x^{2} - 5x + 6 | 42 | 28 | 20 | 12 | 6 | 2 | 0 | 0 | 2 |

2. What are the roots for *y* = *x*^{2} - 5*x* + 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.

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