Final answer:
The vertex of the parabola is (0, -22/7) and the axis of symmetry is x = 0.
Step-by-step explanation:
The given equation is y = (1/28)(x-4)^2 - 5, which is in the form of y = ax^2 + bx + c. Comparing this to the general equation of a parabola, we can see that a = 1/28, b = 0, and c = -5. The vertex of the parabola can be found using the formula x = -b/2a, and substituting the values, we get x = -0/(2*(1/28)) = -0/2 = 0. When we substitute x = 0 into the equation, we get y = (1/28)(0-4)^2 - 5 = (1/28)(16) - 5 = 16/28 - 5 = -3/7 - 5 = -22/7. Therefore, the vertex is (0, -22/7). The axis of symmetry is x = 0.