Solution
Step 1
Write the equation:
[tex]f(x)\text{ = }\frac{1}{2}x^2\text{ + 2x - 6}[/tex]
Step 2
Find the vertex , the intercepts and the plot the graph
[tex]\begin{gathered} \mathrm{Axis\:interception\:points\:of}\:\frac{1}{2}x^2+2x-6:\quad\mathrm{X\:Intercepts}:\:\left(2,\:0\right),\:\left(-6,\:0\right),\: \\ \begin{equation*} \mathrm{Y\:Intercepts}:\:\left(0,\:-6\right) \end{equation*} \\ \\ \\ \mathrm{Vertex\:of}\:\frac{1}{2}x^2+2x-6:\quad \mathrm{Minimum}\:\left(-2,\:-8\right) \end{gathered}[/tex]
