Final answer:
To find the vertex of the quadratic function f(x) = (1/4)x² + 4x + 2, you can use the vertex formula. The vertex is at (-8, 2).
Step-by-step explanation:
The quadratic function is given by f(x) = (1/4)x² + 4x + 2. To find the vertex, we can use the vertex formula, which is x = -b/(2a). In this case, a = 1/4 and b = 4. Plugging these values into the formula, we get x = -4/(2*1/4) = -4/(1/2) = -8.
Now we can find the y-coordinate of the vertex by plugging the x-coordinate into the equation. f(-8) = (1/4)*(-8)² + 4*(-8) + 2 = 32 - 32 + 2 = 2.
Therefore, the vertex of the quadratic function is (-8, 2).