Solving Quadratic Equations - By Graphing

Example: $2x^2 -4x =6$

Step 1: Put all terms on the same side of the equation (Solve for zero)

$2x^2-4x-6=0$

Step 2: Replace the zero with a y

$2x^2-4x-6=y$

Step 3: Make an input/output table

x | $2x^2-4x-6$ | y |
---|---|---|

-2 | $2(-2)^2 - 4(-2) -6$ | 10 |

-1 | $2(-1)^2 - 4(-1)-6$ | 0 |

0 | $2(0)^2 - 4(0) -6$ | -6 |

1 | $2(1)^2 - 4(1) -6$ | -8 |

2 | $2(2)^2 - 4(2) -6$ | -6 |

Step 4: Graph the points

(-2,10)

(-1,0)

(0, -6)

(1, -8)

(2, -6)

Step 5: Estimate the points where the line crosses the x-axis. These are the solutions to the original equation.

Solutions: x= -1, x = 3

page revision: 5, last edited: 29 Apr 2008 17:48