This blog has everything you need to know for drawing and plotting quadratic graphs. In order to plot points, you will need to be confident with substituting into expressions. If you feel you need to revise this first, you can find help on our revision sheets.

Once you’ve mastered drawing quadratic graphs, you may want to move on to plotting cubic and reciprocal graphs.

**Example 1**

Plot the graph of the equation π¦ = π₯Β² + 2π₯ β 3, for -4 β€ π₯ β€ 2.

A good idea is to use a table of values to set out coordinate pairs clearly. The range of π₯-values has been defined in the question as -4, -3, -2, -1, 0, 1 and 2. This will sometimes be set out in a table for you, but just set up your own if not.

For each π₯-value, substitute into the equation given to find the corresponding π¦-value.

For π¦ = π₯Β² + 2π₯ β 3:

π₯ | -4 | -3 | -2 | -1 | 0 | 1 | 2 |

π₯Β² | 16 | 9 | 4 | 1 | 0 | 1 | 4 |

+ 2π₯ | -8 | -6 | -4 | -2 | 0 | 2 | 4 |

β 3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 |

π¦ | 5 | 0 | -3 | -4 | -3 | 0 | 5 |

Once you have a completed table of values, you can plot the coordinates and draw the graph. Plot coordinate pairs with a tidy βΓβ, making sure you use the correct axis for π₯ and π¦-values.

Draw a smooth, freehand curve through the points. You **should never** just join each point like a dot to dot!

**Example 2**

Plot the graph of the equation π¦ = π₯Β² β 3π₯ β 2, for -1 β€ π₯ β€ 4.

As before, we will start by doing a table of values:

π₯ | -1 | 0 | 1 | 2 | 3 | 4 |

π¦ | 2 | -2 | -4 | -4 | -2 | 2 |

Then we plot the points and draw a nice, smooth curve.

Make sure the vertex of your curve is smooth and not flat. If you have two points with the same π¦-value at the bottom/top of your curve, it means neither of these are the lowest/highest point of the curve.

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