Given, \(f ( x ) = 2 x^2 + 8 x + 1\), the zeros are the values of \(x\) which result in an output value of \(y = 0\). Thus the zeros are the solutions of the equation \(2 x^2 + 8 x + 1 = 0\). Using the quadratic formula, we get
\[ x=\frac{-8\pm\sqrt{8^2-4(2)(1)}}{2(2)}=\frac{-8\pm\sqrt{56}}{4}=-2\pm\frac{\sqrt{14}}{2} \]