Question

identify the vertex, then graph

1. $f(x)=|x + 2|+1$
2. $f(x)=-dfrac{5}{2}|x - 4|$

Explanation:

Problem 7: \( f(x) = |x + 2| + 1 \)

Step 1: Recall the vertex form of an absolute value function

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

Step 2: Identify \( h \) and \( k \) from the given function

For \( f(x) = |x + 2| + 1 \), we can rewrite \( x + 2 \) as \( x - (-2) \). So comparing with \( f(x) = a|x - h| + k \), we have \( h = -2 \) and \( k = 1 \).

Step 1: Recall the vertex form of an absolute value function

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

Step 2: Identify \( h \) and \( k \) from the given function

For \( f(x) = -\frac{5}{2}|x - 4| \), we can rewrite it as \( f(x) = -\frac{5}{2}|x - 4| + 0 \). So comparing with \( f(x) = a|x - h| + k \), we have \( h = 4 \) and \( k = 0 \).

Answer:

The vertex of \( f(x) = |x + 2| + 1 \) is \((-2, 1)\)

Problem 8: \( f(x) = -\frac{5}{2}|x - 4| \)