Question

identify the vertex and the axis of symmetry for the function.\\( g(x)=(x - 61)^2 \\)\\( \\)\\( \\)the vertex of the function 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 for \( g(x)=(x - 61)^2 \)

For \( g(x)=(x - 61)^2 \), we can rewrite it as \( g(x)=1(x - 61)^2+0 \). So, \( h = 61 \) and \( k = 0 \).

Step3: Determine the vertex

Using the vertex form, the vertex \((h, k)\) is \((61, 0)\).

Answer:

\((61, 0)\)