Question

identify the vertex and the axis of symmetry for the function.\\( g(x)=(x - 53)^2 \\)\
the vertex of the function is \\( \square \\).\
(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 \( g(x) = (x - 53)^2 \), we can rewrite it as \( g(x) = 1(x - 53)^2 + 0 \). Comparing with the vertex form \( y = a(x - h)^2 + k \), we have \( h = 53 \) and \( k = 0 \).

Answer:

\((53, 0)\)