Consider the following expression:
\(f\left( x \right) = - 3x + 2{\rm{ and }}g\left( x \right) = {x^2} - 2x - 4\)
To find out the intersection of the graphs of the above functions,
\( - 3x + 2 = {x^2} - 2x - 4\)
Simplify the expression as,
\(\begin{array}{c}{x^2} - 2x + 3x - 4 - 2 = 0\\{x^2} + x - 6 = 0\\{x^2} + 3x - 2x - 6 = 0\\x\left( {x + 3} \right) - 2\left( {x - 6} \right) = 0\end{array}\)
\(\left( {x + 3} \right)\left( {x - 2} \right) = 0\)
Therefore,
\(x = - 3,x = 2\)
Use maple to plot the graph as follow,
Hence, the intersection points are\({\left( { - 3,0} \right){\rm{and}}\left( {2,0} \right)}\).
