Question

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

Explanation:

Step1: Recall vertex form of absolute value function

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

Step2: Rewrite given function in vertex form

Given \( y = - 4|x + 2| + 5 \), we can rewrite \( x + 2 \) as \( x - (-2) \). So the function becomes \( y = - 4|x - (-2)| + 5 \).

Step3: Identify h and k

Comparing with \( y = a|x - h| + k \), we have \( h=-2 \) and \( k = 5 \). So the vertex is \((-2, 5)\).

Answer:

\((-2, 5)\) (corresponding to the option \((-2,5)\))