Chapter 2.1, Problem 37E

To determine

To find: To match the function with its graph.

Answer to Problem 37E

The function $g(x)=-2{(x-1)}^2+2$ matches with the graph in option D.

Explanation of Solution

Given information: $g(x)=-2{(x-1)}^2+2$ and six different graphs.

Identifying the vertex:

The given function is in the form of $g(x)=a{(x-h)}^2+k$ ,

Here, $a=2,h=1,k=2$ ,

We know the vertex is $(h,k)$ .

The vertex of the given function $g(x)=-2{(x-1)}^2+2$ is $(1,2)$ .

The given function opens down.

Thus we can conclude that option D is the matching graph for the given function.