Chapter 8.4, Problem 40E

To determine

To analyse: The graph of $g\left(x\right)={\left(x+1\right)}^2-7$

Answer to Problem 40E

The graph of g(x) is a translation left 1 and down 7 of the parent function.

Explanation of Solution

Given information:

The given function as shown below,

  $g\left(x\right)={\left(x+1\right)}^2-7$

Formula used:

The x axis represents the horizontal axis and the y axis represents the vertical axis.

Calculation:

Graph using the vertex, axis of symmetry, and two other points:

Vertex: (-1, -7)

Axis of Symmetry: x = -1

  

Compare to the parent function:

The graph of g(x) is a translation left 1 and down 7 of the parent function.

Conclusion:

The graph of g(x) is a translation left 1 and down 7 of the parent function.