Question

what is the vertex of the following function?
$y=4|x|+1$
$(-4,1)$
$(4,1)$
$(0,1)$
$(4,-1)$

Explanation:

Step1: Recall absolute value form

The parent absolute value function is $y=|x|$, with vertex at $(0,0)$. The transformed form is $y=a|x-h|+k$, where $(h,k)$ is the vertex.

Step2: Match given function to form

For $y=4|x|+1$, we rewrite it as $y=4|x-0|+1$. Here, $h=0$ and $k=1$.

Step3: Identify vertex coordinates

Using $(h,k)$, the vertex is $(0,1)$.

Answer:

(0,1)