Question

Priya says, “once I know the vertex is (4,10), I can find out, without graphing, wether the vertex is maximum or the minimum of function p. 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 Oriya might have reasoned about whether the vertex is the minimum or maximum.

Answer 1

Explanation:

Hello, So use the function p, to find the output

`p(3) = - (3 - 4) {}^(2) + 10 = - 39`

`p(5) = - (5 - 4) {}^(2) + 10 = 9`

Since p(4)>p(5) and p(3), p(4) is the maximum.

Also p is written in vertex form which is

`a(x - h) {}^(2) + k`

Since a is negative, we will have a maximum vertex.

The answer is

Oriya has reasoned the vertex is a maximum because p(4) is the highest points compared to points near it such as p(3) and p(5).