What is the vertex of the absolute value function defined by ƒ(x) = |x - 7| + 1?

Mathematics

2 answers:

Olin [163]2 years ago

8 0

The absolute value function, known as the modulus function, is represented by a v-shaped graph, or a modulus graph. So the graph looks like a V.
Let the vertex point be S.
To find the coordinates of the vertex S, you follow those steps:
First, to find the x of the vertex, you takes what's between the absolute value and make it =0
x - 7 = 0
Add 7 in both sides to get the variable x alone on a side and its value on the other side:
x - 7 + 7 = 0 + 7
x = 7

So S(7;y)

Now to find y, we replace x by its value and do the calculus:
|x - 7| + 1 = |7 - 7| + 1 = 0 + 1 = 1

So S(7;1).

I've added a picture of the graph represented this equation under the answer.

Hope this Helps! :)

BartSMP [9]2 years ago

7 0

The vertex is (-7,1)

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Answer:

$x(x+1)(x-1)$

Step-by-step explanation:

We see that the two terms share an x, so we can pull that out:

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Now notice that we have a difference of squares ( $x^2-1$ ). Given a difference of squares, $a^2-b^2$ , this can always be factored into $(a+b)(a-b)$ . We can use this in this case: $x^2-1=(x+1)(x-1)$ .