Final answer:
The vertex of the quadratic function f(x) = 2x² + 32x + 2017 is (-8, -336).
Step-by-step explanation:
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) represents the coordinates of the vertex.
In the given function f(x) = 2x² + 32x + 2017, we have a = 2, b = 32, and c = 2017.
To find the vertex, we can use the formula for the x-coordinate of the vertex, which is given by x = -b / (2a). Plugging in the values, we have x = -32 / (2 * 2) = -8. To find the y-coordinate of the vertex, we can substitute this value of x into the function: f(-8) = 2(-8)² + 32(-8) + 2017 = -336.
Therefore, the vertex of the function is (-8, -336).