Through which other point must the graph of y pass?

Question

The graph of y=ax²+bx+c passes through the points (1,-8), (2,-1), (3,4), and (5,8). If the maximum value of y occurs at x=5, through which other point must the graph of y pass?

Answer 1

If the maximum y value is 8 when x=5 (vertex), then this is an upside-down parabola (a<0).

 

The other points given are all to the left of the vertex.  By symmetry, (7,4) must also be on the graph, as well as (8,-1) and (9,-8)--each of these points being 'paired' with the three other given points.