Question

find the vertex of the given function. f(x) = |x + 1| - 7 the vertex is at ( , ). done

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Rewrite the given function in vertex form

Given \( f(x)=|x + 1|-7 \), we can rewrite \( x + 1 \) as \( x-(-1) \). So the function becomes \( f(x)=|x-(-1)|+(-7) \).
Comparing with \( f(x) = |x - h| + k \), we have \( h=-1 \) and \( k = -7 \).

Answer:

\((-1, -7)\)