Question

What transformations have been done to the graph of y=x^2 to obtain the graph of y=(-1/2)(x+1)^2-3. Please include direction as well as numerical values.

Answer 1

`y=x^2 \Longrightarrow y=(x+1)^2` shifting 1 unit left

`y=(x+1)^2 \Longrightarrow y=(x+1)^2-3` shifting3 units down

`y=(x+1)^2-3 \Longrightarrow y=(1)/(2)(x+1)^2-3` scaling by factor
`(1)/(2)`

`y=(1)/(2)(x+1)^2-3 \Longrightarrow y=-(1)/(2)(x+1)^2-3` reflecting about the x-axis