Answer
$33$ years old; $58$ years old
Work Step by Step
In order to determine the age group expected to be involved in $3$ fatal crashes per $100$ million miles driven, we solve the equation $f(x)=3$ using the Quadratic Formula:
$$\begin{align*}
0.013x^2-1.19x+28.24&=3\\
0.013x^2-1.19x+28.24-3&=0\\
0.013x^2-1.19x+25.24&=0\\
x&=\dfrac{-(-1.19)\pm\sqrt{(-1.19)^2-4(0.013)(25.24)}}{2(0.013)}\\
&\approx\dfrac{1.19\pm 0.322}{2(0.013)}\\
x_1&\approx 33\\
x_2&\approx 58.
\end{align*}$$
The function models the actual data in a good manner because age $33$ corresponds to a number of fatal crashes higher, but close to $2.8$, while the age $58$ corresponds to a number of fatal crashes higher, but close to $3$.
