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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

User Nischalinn
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\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)

User Joe Niland
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