## Finding the equation of a parabola given the axes intercepts

If we know where a parabola cuts the *‘x’* axes then we can ascertain its two factors. The value of the* ‘y’* intercept will enable us to do the relevant scaling required to get our equation.

Consider a curve that cuts the* ‘x’* axis at -4 and 3 and the ‘y’ axis at 6.

1 | The factors must be (x + 4) and (x -3) |

2 | Let y = a(x + 4)(x – 3) |

3 | a×(4)×(-3) = 6 |

4 | So a = -1/2 |

5 | So y = -1/2(x + 4)(x – 3) |

### Now let’s see another example

The curve cuts the the axes at (2, 0), (4, 0) and (0,16).

1 | The factors must be (x – 2) and (x -4) |

2 | Let y = a(x – 2)(x – 4) |

3 | a×(-2)×(-4) = 16 |

4 | So a = 2 |

5 | So y = 2(x – 2)(x – 4) |

#### Questions to try

- Curve cuts the axes at (-4, 0), (2, 0) and (0,-8)
- Curve cuts the axes at (-2, 0), (4,0) and (0, 8 )
- Curve cuts the axes at (1, 0), (4, 0) and (0, 8 )
- Curve cuts the axes at (-4,0), (-1, 0) and (0, -8)

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