Answer
minimum: $-1.5.$
Work Step by Step
Let us compare $f(x)=2x^2+6x+3$ to $f(x)=ax^2+bx+c$. We can see that $a=2, b=6, c=3$. Since $a\gt 0$, the graph opens up and hence its vertex is a minimum. The minimum value is at $x=-\frac{b}{2a}=-\frac{6}{2\cdot 2}=-1.5.$ Hence, the minimum value is
$f(-1.5)=2(-1.5)^2+6(-1.5)+3=-1.5.$
