A.6.16.2 Sharing a Vertex

Here are two equations that define quadratic functions. The graph of passes through (0, -6) and (4, 10), these point are on the coordinate plane below. Find the coordinates of another point on the graph of , explain how you got your point. Then add your point to the graph along with the other 2 to sketch the graph of .

On the same coordinate plane, identify the vertex and two other points that are on the graph of . Explain your reasoning. Sketch and label the graph of on the same coordinte grid as .

Priya says, "Once I know the vertex is (4, 10), I can find out, without graphing, whether the vertex is the maximum or the minimum of function . I would just compare the coordinates of the vertex with the coordinates of a point on either side of it." Complete the table and then explain how Priya might have reasoned about whether the vertex is the minimum or maximum.