Answer
See graph
Work Step by Step
Factor out the coefficient of $x^2$ and square half of the coefficient of the $x$-term: $(-40 / 2)^2=400$. Adding and subtracting this number after the $x$-term gives
$$
\begin{aligned}
& y=26+0.4 x-0.01 x^2 \\
& y=-0.01\left(x^2-40 x-2600\right) \\
& y=-0.01\left(x^2-40 x+20^2-2600-400\right) \\
& y=-0.01(x-20)^2+30
\end{aligned}
$$
i) The vertex is $(20,30)$ and the axis of symmetry is $x=20$.
ii) From the original equation, the $y$-intercept is $y= 26$.
iii) We find the $x$-intercepts by solving $y=0$
$$
\begin{aligned}
-0.01(x-20)^2+30 & =0 \\
-0.01(x-20)^2 & =-30 \\
(x-20)^2 & =3000 \\
x-20 & = \pm \sqrt{3000} \\
x & =20 \pm \sqrt{3000},
\end{aligned}
$$
or
$$
x=74.7723 \ldots, x=-34.7723
$$
