Question

question 14 of 22
which of the following functions is graphed below?

a. ( y = |x + 8| + 2 )
b. ( y = |x - 8| + 2 )
c. ( y = |x - 8| - 2 )
d. ( y = |x + 8| - 2 )

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Identify the vertex from the graph

From the given graph, we can see that the vertex (the point of the "V") is at \((8, 2)\).

Step3: Substitute \( h \) and \( k \) into the vertex form

For the vertex \((h,k)=(8,2)\), substituting into \( y = |x - h| + k \), we get \( y=|x - 8|+2 \).

We can also check the other options:

• For option A: \( y = |x + 8|+2=|x-(- 8)| + 2\), its vertex is at \((-8,2)\), which does not match the vertex of the given graph.
• For option C: \( y=|x - 8|-2\), its vertex is at \((8,-2)\), which does not match the vertex of the given graph.
• For option D: \( y = |x + 8|-2=|x-(-8)|-2\), its vertex is at \((-8,-2)\), which does not match the vertex of the given graph.

Answer:

B. \( y = |x - 8| + 2 \)