Step 2 of 2: Use the quadratic formula $f(x)=2 x^{2}+4 x-1$ to determine the coordinates of the vertex of the best-fitting parabola. Write the exact answer. Do not round.

Step 1 ：Given the quadratic function \(f(x)=2 x^{2}+4 x-1\), we are to find the coordinates of the vertex of the best-fitting parabola.

Step 2 ：The vertex of a parabola given by the equation \(f(x)=ax^{2}+bx+c\) is given by the point \(-\frac{b}{2a}, f(-\frac{b}{2a})\).

Step 3 ：In this case, \(a=2\), \(b=4\), and \(c=-1\).

Step 4 ：We calculate the x-coordinate of the vertex as \(-\frac{b}{2a} = -1.0\).

Step 5 ：We then substitute this value into the equation to find the y-coordinate, which is \(-3.0\).

Step 6 ：Final Answer: The coordinates of the vertex of the best-fitting parabola are \(\boxed{(-1, -3)}\).