To determine the vertex form of a parabola has equation:
[tex]f(x)=a(x-h)^2+k[/tex]where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.
From the question, we have that, the vertex is (-1, 1)
and the leading coefficient is a = 2
We substitute the vertex and the leading coefficient into the vertex form to
get:
[tex]\begin{gathered} f(x)=2(x+1)^2\text{+}1 \\ f(x)=2(x+1)^2+1 \end{gathered}[/tex]The graph of this function is shown in the attachment.
Hence the equation of parabola is
[tex]f(x)=2(x+1)^2+1[/tex]
