Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Find the vertex of the given function:

[tex]\( f(x) = |x + 1| - 7 \)[/tex]

The vertex is at [tex]\(\square, \square\)[/tex].

Sagot :

GinnyAnswer
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].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.