Question

Identify the graph of g(x)=(x−7)2−1. Then identify the vertex and axis of symmetry.

Answer 1

The line of the symmetry x=7

The vertex (7,-1)

Explanation:

The graph of the function
`g(x)=(x-7)^2-1` is a parabola (see attached diagram for details)

Consider the parent function
`f(x)=x^2.` To get the graph of the function g(x), we need to translate the graph of the function f(x) seven units to the right and 1 unit down.

The line of the symmetry of the parent function is x=0 and the vertex is at (0,0). After the translation, the line of the symmetry becomes x=7 and the vertex (7,-1).