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)=\\(g(x)=(x - 5)^2 - 4\\)\
the vertex is (5, - 4)\
(type an ordered pair.)\
the axis of symmetry is x = 5\
(type an equation.)\
the graph opens

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \( g(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex, \(x = h\) is the axis of symmetry, and the direction of opening is determined by the sign of \(a\). If \(a>0\), the parabola opens upward; if \(a < 0\), it opens downward.

Step2: Identify the value of \(a\) in \(g(x)=(x - 5)^2-4\)

In the function \(g(x)=(x - 5)^2-4\), we can rewrite it as \(g(x)=1\times(x - 5)^2-4\), so \(a = 1\).

Step3: Determine the direction of opening

Since \(a=1>0\), the parabola opens upward.

Answer:

upward