Finding the Vertex of a Quadratic Function

Consider the quadratic function defined by the equation:

$$ f(x) = ax^2 + bx + c $$

where the coefficients are given as follows:

• $$ a = 2 $$
• $$ b = -4 $$
• $$ c = 1 $$

To determine the vertex of the parabola represented by this function, use the vertex formula:

$$ x_{vertex} = -\f\frac{b}{2a} $$

Find the $y$-coordinate of the vertex by substituting $x_{vertex}$ back into the function. What is the vertex of the quadratic function given by $f(x)$?