A quadratic equation can sometimes be solved by drawing its graph on a set of xy coordinate axes and then seeing where the graph meets the x-axis.

**Example**

Using a graph, solve for x:

2x^{2} - 3x - 14 = 0

**Answer**

First we draw the line of y = 2x^{2} - 3x - 14 and find the x-values for when y = 0.

In other words, we are looking for where the line y = 2x^{2} - 3x - 14 and y = 0 (the x-axis) meet.

These will be the points where y = 2x^{2} - 3x - 14 crosses the x-axis.

*NB. If the curve does not cross the x-axis, then there will be no real solutions to this equation.*

To plot y = 2x^{2} - 3x - 14 use a table, choose x-values and work out the y-values.

x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 3½ | |

y = 2x^{2} - 3x - 14 |
0 |
-9 | -14 | -15 | -12 | -5 | 6 | |
0 |

When we plot these as (x, y) coordinates we get a parabola which looks like this:

The intercepts on the x-axis are at (-2, 0) and (3½, 0)

Solution is:

**x = -2 or x = 3½**