Answer
multiple answers; see details
Work Step by Step
The standard form of the equation $
y=-3x^2+\dfrac{1}{2}x+4
$ is
\begin{array}{l}
2y=-6x^2+x+8\text{... multiply both sides by $2$}\\\\
2y-8=-6\left(x^2-\dfrac{1}{6}x\right)\\\\
2y-8-\dfrac{1}{24}=-6\left(x^2-\dfrac{1}{6}x+\dfrac{1}{144}\right)\\\\
2y-\dfrac{193}{24}=-6\left(x-\dfrac{1}{12}\right)^2\\\\
-\dfrac{2}{6}y-\dfrac{193}{24(-6)}=\left(x-\dfrac{1}{12}\right)^2\\\\
\left(x-\dfrac{1}{12}\right)^2=-\dfrac{1}{3}y+\dfrac{193}{144}\\\\
\left(x-\dfrac{1}{12}\right)^2=-\dfrac{1}{3}\left(y-\dfrac{193}{48}\right)
.\end{array}
The graph of this equation is a $\text{
parabola
}$ with the following properties:
\begin{array}{l}
\text{Vertex: }\left(
\dfrac{1}{12},\dfrac{193}{48}
\right),\\\\\text{Opening:
down
}.\end{array}
Using the properties above, the graph of the equation is given below.
