We start with the dotted line. The first thing that must be done is to find the equation of the line. The equation of the line is y = -x. This means there are two option for the answer. Either it is y > -x or y < -x. Let us pick any point in the shaded area. We pick (2,4). Clearly our answer is y > -x since 4 > -2.
We repeat this for the solid line. The equation of the line is y = 0.5x - 2. Again we get a test point in the shaded region (2,1). This point tells us that the shaded region y ≥ 0.5x - 2 since 1 ≥ 0.5(2) - 2.
Vertex form is written in this format: f(x) = a(x - h) + k. The vertex point is written in the form (h,k). To write the vertex in the equation, fill in the digits where they belong.