#### Topic Content:

- Quadratic Graph

In order to achieve using the graphical method to solve simultaneous equations including one linear and one quadratic, we need to plot the graph of each equation on the same axes.

Then mark off the x and y coordinates of the point of intersection of both curves to obtain the required solution.

### Example 1.1.1:

**(a)** Copy and complete the following table of values for the relation

y = 2 + x – x^{2}

x | -2 | -1.5 | -1 | -0.5 | 0 | 0.5 | 1.0 | 1.5 | 2 | 2.5 | 3.0 |

y | – | – | 0 | 1.25 | 2 | – | 2 | 1.25 | – | – | -4 |

**(b)** Draw the graph of the relation, using a scale of 2 cm to 1 unit on each axis.

**(c)** Using the same axes, draw the graph of y = 1 – x.

**(d)** Use your curves to find the solution of the equation 1 + 2x â€“ x^{2} = 0 **(SSCE)**.

**Solution:**

**(a)** y = 2 + x – x^{2}

x | -2 | -1.5 | -1 | -0.5 | 0 | 0.5 | 1.0 | 1.5 | 2 | 2.5 | 3.0 |

y | -4 | -1.75 | 0 | 1.25 | 2 | 2.25 | 2 | 1.25 | 0 | -1.75 | -4 |

**(b)** & **(c)** y = 1 – x

X | -2 | -1 | 0 | 1 | 2 | 3 |

Y | 3 | 2 | 1 | 0 | -1 | -2 |

**Diagram of a Quadratic graph **

**Scale: **1 unit â‰¡ 2 cm on both axes.

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