To find the vertex of the quadratic function \(y = 2x^2 - 12x + 8\), we can use the vertex formula for a parabola defined by \(y = ax^2 + bx + c\). The x-coordinate of the vertex can be found using the formula:
\[ x = -\frac{b}{2a} \]
In this equation, \(a = 2\) and \(b = -12\). Plugging in these values, we get:
\[ x = -\frac{-12}{2 \cdot 2} = \frac{12}{4} = 3 \]
Next, we will find the y-coordinate by substituting \(x = 3\) back into the original equation:
\[ y = 2(3)^2 - 12(3) + 8 \] \[ y = 2(9) - 36 + 8 \] \[ y = 18 - 36 + 8 \] \[ y = 18 - 36 + 8 = -10 \]
Thus, the vertex of the parabola is at the point:
\[ (3, -10) \]
The correct response is:
(3, -10)