Answer:
Your idea of building a table is not a bad start if you want accurate points.
Else, it's a parabola. It's y intercept has the non-zero coordinate equal to the constant term (red dot on the graph).
It's x intersects you find by solving
[tex]2x^2+12x+4 = 0 \rightarrow x^2+6x+2=0\\ x_1_,_2= -3\pm\sqrt7\\x_1\approx -0.35\\x_2\approx-5.35[/tex]
(green dots).
Simmetry axis has equation [tex]x=-\frac{b}{2a} = -\frac{12}{4}=-3[/tex] (orange line).
Vertex sits on this line and is in the parabola, so it's other coordinate is
[tex]2(-3)^2+12(-3)+4= -14[/tex] (orange dot).
At that point you either continue with the table, or you go for a "good enough" and try to draw a better looking parabola than mine.
