### Quadratic Equations – Exercise 9.9 – Question:

- Draw the graphs of the following quadratic equations:

(i) y = – x^{2}

(ii) y = 3x^{2}

(iii) y = ^{1}/_{2} x^{2} – 2

(iv) y = x^{2} – 2x

(v) y = x^{2} – 8x + 7

(vi) y = (x + 2)(2 – x)

(vii) y = x^{2} + x – 6

(viii) y = x^{2} – 2x + 5

## Quadratic Equations – Exercise 9.9 – Solution:

**Draw the graphs of the following quadratic equations:**

**(i) y = – x ^{2}**

Solution:

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

y | -9 | -4 | -1 | 0 | -1 | -4 | -9 |

** (ii) y = 3x ^{2}**

Solution:

x | -2 | -1 | 0 | 1 | 2 |

y | 12 | 3 | 0 | 3 | 12 |

** (iii) y = ^{1}/_{2} x^{2} – 2**

Solution:

x | -2 | -1 | 0 | 1 | 2 |

y | 0 | –^{3}/_{2} |
-2 | –^{3}/_{2} |
0 |

** (iv) y = x ^{2} – 2x = x(x – 2)**

Solution:

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

y | 8 | 3 | 0 | -1 | 0 | 3 |

** (v) y = x ^{2} – 8x + 7**

Solution:

x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

y | 16 | 7 | 0 | -5 | -8 | -9 | -8 | -5 | 0 | 7 | 16 |

(vi) y = (x + 2)(2 – x)

Solution:

y = (x + 2)(2 – x) = 2x – x^{2} + 4 – 2x = -x^{2} + 4

Therefore, y = -x^{2} + 4

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

y | -5 | 0 | 3 | 4 | 3 | 0 | -5 |

** (vii) y = x ^{2} + x – 6**

Solution:

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

y | 6 | 0 | -4 | -6 | -6 | -4 | 0 | 6 |

** (viii) y = x ^{2} – 2x + 5**

Solution:

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

y | 13 | 8 | 5 | 4 | 5 | 8 | 13 |