Answer :
Let's find the vertex of the function [tex]\( f(x) = |x + 1| - 7 \)[/tex].
The general form of an absolute value function is [tex]\( f(x) = |x - h| + k \)[/tex], where [tex]\((h, k)\)[/tex] represents the vertex of the function.
Step 1: Start by rewriting the given function in the form that reveals the vertex easily.
Given [tex]\( f(x) = |x + 1| - 7 \)[/tex], we compare it with the general form [tex]\( f(x) = |x - h| + k \)[/tex].
Step 2: Identify the values for [tex]\(h\)[/tex] and [tex]\(k\)[/tex].
Here, the expression inside the absolute value is [tex]\(x + 1\)[/tex]. We need to rewrite it to match the form [tex]\(x - h\)[/tex]. Notice that:
[tex]\[ x + 1 = x - (-1) \][/tex]
So, [tex]\(h = -1\)[/tex].
Now, looking at the constant term outside the absolute value, we have [tex]\( -7 \)[/tex]. So, [tex]\( k = -7 \)[/tex].
Step 3: Combine our values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] to find the vertex.
The vertex of the function is at:
[tex]\[ (h, k) = (-1, -7) \][/tex]
Thus, the vertex of the function [tex]\( f(x) = |x + 1| - 7 \)[/tex] is at [tex]\( (-1, -7) \)[/tex].
The vertex is at [tex]\(-1, -7\)[/tex].
The general form of an absolute value function is [tex]\( f(x) = |x - h| + k \)[/tex], where [tex]\((h, k)\)[/tex] represents the vertex of the function.
Step 1: Start by rewriting the given function in the form that reveals the vertex easily.
Given [tex]\( f(x) = |x + 1| - 7 \)[/tex], we compare it with the general form [tex]\( f(x) = |x - h| + k \)[/tex].
Step 2: Identify the values for [tex]\(h\)[/tex] and [tex]\(k\)[/tex].
Here, the expression inside the absolute value is [tex]\(x + 1\)[/tex]. We need to rewrite it to match the form [tex]\(x - h\)[/tex]. Notice that:
[tex]\[ x + 1 = x - (-1) \][/tex]
So, [tex]\(h = -1\)[/tex].
Now, looking at the constant term outside the absolute value, we have [tex]\( -7 \)[/tex]. So, [tex]\( k = -7 \)[/tex].
Step 3: Combine our values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] to find the vertex.
The vertex of the function is at:
[tex]\[ (h, k) = (-1, -7) \][/tex]
Thus, the vertex of the function [tex]\( f(x) = |x + 1| - 7 \)[/tex] is at [tex]\( (-1, -7) \)[/tex].
The vertex is at [tex]\(-1, -7\)[/tex].
