Question

what is the vertex of the following function?
$y=-4|x+2|+5$
$(2,5)$
$(-2,5)$
$(-4,2)$
$(-4,-2)$

Explanation:

Step1: Recall absolute value form

The vertex form of an absolute value function is $y=a|x-h|+k$, where $(h,k)$ is the vertex.

Step2: Rewrite given function

Rewrite $y=-4|x+2|+5$ as $y=-4|x-(-2)|+5$.

Step3: Identify h and k

Compare with vertex form: $h=-2$, $k=5$.

Answer:

(-2,5)