a) The vertex is the highest/lowest point of a parabola. Therefore, the vertex of this parabola is (1,2).
b) Find a point where it lies on an integer for both the x and y axis. You could use (3,1), (-1,1), (-2,0), etc.
c) The formula for a quadratic function given a vertex and a point is:
y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
Plugging in our point for the vertex, we get:
y = a(x-1)^2 + 2.
We can use one of the points to solve for a.
1 = a(3-1)^2 + 2
1 = a(2)^2 + 2
1 = a(4) + 2
1 = 4a + 2
-1 = 4a
a = -1/4
Since we now know a, let's rewrite the equation.
y = (-1/4)(x-1)^2 + 2