Answer
(a) $f(x)=0.0203x^2+353$
(b) $2304\ ppm$
Work Step by Step
(a) As $(0,353)$ is the vertex, use the model equation $f(x)=a(x-h)^2+k$, we have $0-h=0$, thus $h=0$ and $f(0)=k=353$
Use point $(285,2000)$, we have $a(285)^2+353=2000$, thus $a=\frac{2000-353}{285^2}\approx0.0203$
Thus the function $f(x)=0.0203x^2+353$
(b) For year 2300, we have $x=2300-1990=310$, thus $f(310)=0.0203(310)^2+353\approx2304\ ppm$
