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 $f(x)=x^{2}$.
$g(x)=(x - 1)^{2}-6$
the vertex is \square.
(type an ordered pair)

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Identify h and k from \( g(x)=(x - 1)^2 - 6 \)

In the function \( g(x)=(x - 1)^2 - 6 \), we can see that \( h = 1 \) and \( k = -6 \) by comparing with the vertex form \( a(x - h)^2 + k \) (here \( a = 1 \)).

Answer:

\((1, -6)\)