Answer:
the vertex is (-3 , -3)
Step-by-step explanation:
[tex]\frac{1}{2} x^{2}+3x+\frac{3}{2}[/tex]
[tex]=\frac{1}{2} \left( x^{2}+6x+3\right)[/tex]
[tex]=\frac{1}{2} \left[ \left( x+3\right)^{2} -9+3\right][/tex]
[tex]=\frac{1}{2} \left( x+3\right)^{2} -3[/tex]
then the vertex is (-3 , -3)
