Suppose we are asked to sketch the graph y = x2 +3x - 8
To do this we would plot a table of values for x and y-coordinates:
| x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 |
| y | 2 | -4 | -8 | -10 | -10 | -8 | -4 | 2 |
We would then plot these coordinates using a nice smooth curve. You should get a regular curve, that resembles a smile. If you don't then you have made a mistake with some of your calculations above
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The solution to the equation y = x2 + 3x -8 = 0 is where the curve hits/touches the x-axis.
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We can then use this graph to solve other equations.
Suppose we wanted to solve x 2 + x -8 =0
If we add 2x to both sides of the equation we get
x 2 + 3x - 8 = 2x
The left hand side is our original graph and the right hand side is a new graph.
We therefore plot the graph y = 2x over our original graph y = x2 + 3x - 8.
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The solution to the equation y = x2 + x -8 = 0 is where the two lines intersect.
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We can plot the actual graph y = x2 + x - 8 to confirm this
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The solution to the equation y = x2 + x -8 = 0 is where the graph hits the x-axis.
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