Question

how can you write an absolute value equation so that the vertex will be at (-5,-7)?
y = |x - 7| - 5
y = |x + 7| - 5
y = |x + 5| - 7
y = |x - 5| - 7

Explanation:

Step1: Recall absolute value vertex form

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

Step2: Substitute vertex \((-5, -7)\)

Here, \( h = -5 \) and \( k = -7 \). Substituting into the form: \( y = |x - (-5)| + (-7) \), which simplifies to \( y = |x + 5| - 7 \).

Step3: Match with options

Check the options: the third option is \( y = |x + 5| - 7 \), which matches the derived equation.

Answer:

C. \( y = |x + 5| - 7 \) (assuming the third option is labeled C; if the options are in order as shown, the third one: \( y = |x + 5| - 7 \))