Consider (h; k); (x0; y0) 2 R2. Here R2 is set of all ordered pairs (x; y) such that x; y 2 R.
Part I
1. Prove given statement: If x0 = h; y0 = k then there exists the parabola, f, with vertex (h; k), that goes through (x0; y0).
2. Determine the explicit formula for parabola f in part (1).
3. Describe in your own words why given is NOT true: If x0 = x1 = h and y0 = y1 = k then there exists the parabola, F, with vertex (h; k) that goes through (x0; y0) and (x1; y1).
4. Describe in your own words why given is true: If x0 = x1 = h and y0 = y1 = k then there exists the parabola, H, that goes through (h; k); (x0; y0) and (x1; y1)