Question

identify the vertex, axis of symmetry, and direction of the graph of each function. compare the width of the graph to the width of the graph of ( f(x)=x^2 ).
( g(x)=(x - 1)^2 - 1 )
the vertex is
(type an ordered pair )

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Step2: Identify \(h\) and \(k\) from the given function

For the function \( g(x) = (x - 1)^2 - 1 \), we can compare it with the vertex form \( y = a(x - h)^2 + k \). Here, \( h = 1 \) and \( k = -1 \).

Answer:

\((1, -1)\)