Question 3 Given the parametric equations below, eliminate the parameter $t$ to obtain an equation for $y$ as a function of $x$ \[ \begin{array}{l} \left\{\begin{array}{l} x(t)=4 \sqrt{t} \\ y(t)=8 t+5 \end{array}\right. \\ y(x)= \end{array} \]

Step 1 ：Given the parametric equations \(x(t)=4 \sqrt{t}\) and \(y(t)=8 t+5\)

Step 2 ：Express \(t\) in terms of \(x\) from the equation \(x(t)=4 \sqrt{t}\), we get \(t = \frac{x^2}{16}\)

Step 3 ：Substitute \(t\) in the equation for \(y(t)\) with \(\frac{x^2}{16}\) to get \(y(x)\)

Step 4 ：Simplify the equation to get the final answer

Step 5 ：\(\boxed{y(x) = \frac{x^2}{2} + 5}\)