Question

How do i solve this problem I’ve been trying for a while

Answer 1

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

`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`

(green dots).

Simmetry axis has equation
`x=-(b)/(2a) = -(12)/(4)=-3` (orange line).

Vertex sits on this line and is in the parabola, so it's other coordinate is

`2(-3)^2+12(-3)+4= -14` (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.