Question

graph the equation.
$y = 4|x - 4|$

Explanation:

Step1: Identify vertex of absolute value

The vertex of $y=a|x-h|+k$ is $(h,k)$. For $y=4|x-4|$, $h=4, k=0$, so vertex is $(4, 0)$.

Step2: Find point for $x>4$

Let $x=5$, substitute into equation:
$y=4|5-4|=4(1)=4$
Point: $(5, 4)$

Step3: Find point for $x<4$

Let $x=3$, substitute into equation:
$y=4|3-4|=4(1)=4$
Point: $(3, 4)$

Step4: Plot points and draw graph

Plot vertex $(4,0)$, $(5,4)$, $(3,4)$, then draw two straight lines from the vertex through each point, forming a V-shape.

Answer:

The graph is a V-shaped absolute value function with vertex at $(4, 0)$, passing through $(3, 4)$ and $(5, 4)$, opening upwards with a slope of $4$ for $x>4$ and $-4$ for $x<4$.