Question

I'm on my phone so ¦ is absolute value. The graph of y=-2¦x¦ is the graph of y=¦x¦ vertically stretched by a factor of -2 and then reflected over the x-axis. What vertex does this graph have and what two points does it pass through y=-2¦x¦
Please help and explain why!!

Answer 1

well, just looking at the absolute expression, what value for "x" would make |x| equals to 0?

Answer 2

Well the absolute value is distance so how can ¦x¦ equal 0 unless x itself was 0

Answer 3

right so in this case, just setting "x" to 0, since it's the only thing inside the absolute expression, will make it 0, thus
\(\bf y = -2|x| \implies y = -2|x| + 0\\
y = -2|(\color{red}{0})| + \color{red}{0}\\
(\color{red}{0}, \color{red}{0}) \Leftarrow vertex \)

Answer 4

as far as the 2 points, well, just pick a value for "x", and get "y" twice