Suppose you have already plotted P

_{1}: y = x^{2}- 3x + 1, but the teacher asks you to find graphically the roots of P_{2}: y = x^{2}- 4x + 3. What a bother – now you need to plot another parabola. Or do you?Johnny can rearrange P

_{2}to get an equation of the form: sloped line = parabola already plotted. 0 = x ^{2 }- 4x + 3 | Given P _{2} |

+x =( x ^{2} - 4x + 3) +x | Add 'x' to both sides |

x = x ^{2} - 3x + 3 | Simplify by collecting ‘x’ terms on the right |

x - 2 = (x ^{2} - 4x + 3) - 2 | Add '-2' to both sides, i.e., subtract |

x - 2 = x ^{2} - 3x + 1 | Simplify by collecting constant terms on the right |

line = given P _{1} | |

Now Johnny has a sloped line = parabola that he has already graphed

The sloped line has m = 1 and c = -2, so it is easy to draw.

Reading from the graph, the solution to the teacher’s question is x = 1 or x = 3.

As a check, Mary factorises y= x

^{2}- 4x + 3y = (x – 3) (x – 1)

When y = 0,

x – 3 = 0, so x = 3

or x – 1 = 0 so x = 1

Done!

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