Answer
$x = 0$, $x = 0.3$
Work Step by Step
We solve the equation for $x$ when $y=0$:
$$\begin{align*}
y&=-16x^2+4.8x&&\text{Write equation.}\\
0&=-16x^2+4.8x&&\text{Substitute }0\text{ for }y.\\
0&=x(x-0.3)&&\text{Factor out }-16x.\\
x&=0\text{ or }x-0.3=0&&\text{Zero-Product Property.}\\
x&=0\text{ or }x=0.3&&\text{Solve for }x.
\end{align*}$$ This means that it takes $0.3$ seconds for the penguin to perform a complete porpoising.
