Question

1. consider the function $f(x)=|x + 5|$.

10a does the graph of the function open upwards or downwards?
the correct option was a
upwards a
downwards
5 you got it!
10b state the coordinates of the vertex.
vertex = enter your next step here

Explanation:

Step1: Recall the vertex form of absolute value function

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

Step2: Rewrite the given function

The given function is \( f(x) = |x + 5| \), which can be rewritten as \( f(x) = |x - (-5)| + 0 \).

Step3: Identify the vertex coordinates

By comparing with the general form \( f(x) = |x - h| + k \), we can see that \( h = -5 \) and \( k = 0 \). So the vertex of the function \( f(x) = |x + 5| \) is at the point \((-5, 0)\).

Answer:

\((-5, 0)\)