Answer
Graph of $f(x)=\dfrac{1}{3}(x-1)^2+2$
Work Step by Step
Substituting values of $x$ in the given function, $
f(x)=\dfrac{1}{3}(x-1)^2+2
$, results to
\begin{array}{c|c|c}
\text{If }x=-2: & \text{If }x=1 & \text{If }x=4
\\\\
f(x)=y=\dfrac{1}{3}(x-1)^2+2 & f(x)=y=\dfrac{1}{3}(x-1)^2+2 & f(x)=y=\dfrac{1}{3}(x-1)^2+2
\\\\
y=\dfrac{1}{3}(-2-1)^2+2 & y=\dfrac{1}{3}(1-1)^2+2 & y=\dfrac{1}{3}(4-1)^2+2
\\\\
y=\dfrac{1}{3}(9)+2 & y=\dfrac{1}{3}(0)+2 & y=\dfrac{1}{3}(9)+2
\\\\
y=3+2 & y=0+2 & y=3+2
\\\\
y=5 & y=2 & y=5
.\end{array}
Connecting the points $
\left(-2,5\right),
\left(1,2\right),
\text{ and }
\left(4,5\right)
$ with a curve gives the graph of $
f(x)=\dfrac{1}{3}(x-1)^2+2
$.
