We have the next function
[tex]f(x)=2x^2+8x+3[/tex]To find the vertex we mus use the next formula
[tex]x=-\frac{b}{2a}[/tex]Where,
- b is the constant that multiplies x
- a is the constant that multiplies x^2
So, the x coordinate of the vertex is
[tex]x=-\frac{8}{2(2)}=-2[/tex]And, the y coordinate of the vertex would be
[tex]\begin{gathered} y=2(-2)^2+8(-2)+3 \\ y=-5 \end{gathered}[/tex]Then, the vertex is (-2, -5)
Finally, the graph would be
