Question

sketch the graph of the quadratic function and the axis of symmetry. state the vertex, and give the equation for the axis of symmetry.
$f(x) = (x - 4)^2$
use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
the vertex is (4,0).
(type an ordered pair)
the axis of symmetry is $x = 0$
(type an equation)

Explanation:

Step1: Recall the vertex form of a quadratic function

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex and the axis of symmetry is \( x = h \).
For the function \( f(x)=(x - 4)^2 \), we can rewrite it as \( f(x)=1\times(x - 4)^2+0 \). So, by comparing with the vertex form, \( h = 4 \) and \( k = 0 \).

Step2: Determine the vertex

From the vertex form analysis, the vertex \((h,k)\) is \((4,0)\).

Step3: Determine the axis of symmetry

The axis of symmetry for a quadratic function in vertex form \( f(x)=a(x - h)^2 + k \) is the vertical line \( x = h \). Since \( h = 4 \), the axis of symmetry is \( x = 4 \).

Answer:

The vertex is \((4,0)\). The axis of symmetry is \( x = 4 \).