Question

1. consider the function $f(x)=|x + 5|$. downwards 5 you got it! 10b state the coordinates of the vertex. vertex = $(-5, 0)$ 5 nailed it! 10c state the equation of the line of symmetry. enter your next step here

Explanation:

Step1: Recall properties of absolute value functions

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

Step2: Identify \( h \) from the given function

For the function \( f(x) = |x + 5| \), we can rewrite it as \( f(x) = |x - (-5)| + 0 \). Here, \( h = -5 \) and \( k = 0 \).

Step3: Determine the line of symmetry

Using the property of the absolute value function, the line of symmetry is \( x = h \). Substituting \( h = -5 \), we get the line of symmetry as \( x = -5 \).

Answer:

The equation of the line of symmetry is \( x = -5 \)