Question

Which of the following equations has the vertex (-4, -5)?y = 5|x + 5| - 4y = -4|x – 4| -5y = -5|x – 4| + 5y = 4|x + 4| - 5

Answer 1

$\begin{equation*} y=\:4\left|x+4\right|-5 \end{equation*}$

1) Since the absolute value function, can be written as:

$y=a|x-b|+c$

2) We can tell the absolute value function that has a vertex located at (-4,-5) we need to have the following:

$\begin{gathered} |x+4|=0 \\ x+4=0 \\ x=-4 \\ \\ y=4|x+4|-5 \\ \\ y=4\lvert-4+4\rvert-5 \\ \\ y=4(0)-5 \\ \\ y=-5 \end{gathered}$

3) Hence, the answer is:

$y=\:4\left|x+4\right|-5,\Rightarrow V(-4,-5)$