How does a change in the value of h affect the axis of symmetry of the graph? How does the value of k change the axis of symmetry?

The value of h is exactly the axis of symmetry. So when h changes, it completely changes the line of symmetry. This is because the vertex is (h, k) and the x value of the vertex is always equal to the line of symmetry in a quadratic.

Changing the k value does nothing to the line of symmetry. This is because it is just moving the graph up and down, which doesn't change the symmetry of a parabola.