# How to draw a quadratic graph (a curve or parabola). Like y=x^2 -2x -5

To plot a graph of the form y = ax² + bx + c, first you need to work out the y coordinate in the range specified. To do this all you need to do is substitute the x coordinates into your formula. Be careful with the x² and remember that if you square a negative number you get a positive number.

**Example 1**

Plot the graph of y = 2x² -6, between x = -3 and x = 3

Some of the y coordinates have already been calculated.

Start with x =2, as this will be easier to calculate than x = -3.

To find the y value, substitute x = 2 into your formula:

y = 2 × 2² - 6

y = 2 × 4 -6

y = 2

Now substitute x = 2 into your formula:

y = 2 × (-3)² -6

y =2 × 9 – 6

y = 18 – 6

y = 12

All you need to do now is plot your points and draw the graph. The graph should be curved so don’t use your ruler. This type of curve is known as a parabola.

**Example 2**

Plot the graph of y = x² -2x - 5, between x = -3 and x = 3

Some of the y coordinates have already been calculated.

Start with x =3, as this will be easier to calculate than x = -2.

Like example 1, to find the y value, substitute x = 3 into your formula:

y = x² -2x - 5

y = 3² -2 × 3 – 5

y = 9 – 6 - 5

y = -2

Now substitute x = -2 into your formula:

y = x² -2x – 5

y = (-2)² -2 x -2 - 5

y =4 + 4 – 5

y = 8 – 5

y = 3

All you need to do now is plot your points and draw the graph. Again, the graph should come out as a parabola.

For some more help on grapghs try these hubs:

Straight line graphs from 2 points. Maths help on graphs.

How to plot a horizontal or vertical line like x = 4 or y = -2

Straight line graphs. How to plot a sloping line in math using a table of values.

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