A.6.16.2 Sharing a Vertex

Here are two equations that define quadratic functions.[br][br][math]p\left(x\right)=-\left(x-4\right)^2+10[/math][br][math]q\left(x\right)=\frac{1}{2}\left(x-4\right)^2+10[/math][br][br][br]The graph of [math]p[/math] passes through (0, -6) and (4, 10), these point are on the coordinate plane below.[br][br]Find the coordinates of another point on the graph of [math]p[/math], explain how you got your point.[br]Then add your point to the graph along with the other 2 to sketch the graph of [math]p[/math].
On the same coordinate plane, identify the vertex and two other points that are on the graph of [math]q[/math]. Explain your reasoning. Sketch and label the graph of [math]q[/math] on the same coordinte grid as [math]p[/math].
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 [math]p[/math]. I would just compare the coordinates of the vertex with the coordinates of a point on either side of it." [br][br]Complete the table and then explain how Priya might have reasoned about whether the vertex is the minimum or maximum.
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– Katie Akesson

Information: A.6.16.2 Sharing a Vertex