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.
Using a graph, solve for x:
2x2 - 3x - 14 = 0
First we draw the line of y = 2x2 - 3x - 14 and find the x-values for when y = 0.
In other words, we are looking for where the line y = 2x2 - 3x - 14 and y = 0 (the x-axis) meet.
These will be the points where y = 2x2 - 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 = 2x2 - 3x - 14 use a table, choose x-values and work out the y-values.
| y = 2x2 - 3x - 14
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)
x = -2 or x = 3½