Answer
multiple answers; see details
Work Step by Step
The standard form of the equation $
x=\dfrac{1}{2}y^2+2y+1
$ is
\begin{array}{l}
2x=y^2+4y+2\text{... multiply both sides by $2$}\\\\
2x-2=y^2+4y\\\\
2x-2+4=y^2+4y+4\\\\
2x+2=(y+2)^2\\\\
(y+2)^2=2(x+1)
.\end{array}
The graph of this equation is a $\text{
parabola
}$ with the following properties:
\begin{array}{l}
\text{Vertex: }(
-1,-2
),\\\\\text{Opening:
right
}.\end{array}
Using the properties above, the graph of the equation is given below.
