Answer:
The correct option is the last one.
Step-by-step explanation:
To transform the graph of [tex]y = x ^ 2[/tex] into [tex]y = -2(x - 2) ^ 2 + 2[/tex] the following steps are fulfilled:
1) Move the graph 2 units to the right:
Let [tex]y = f (x-2)[/tex] then [tex]y =(x-2) ^ 2[/tex] Notice that the cut point has been moved to x = 2.
2) Reflect on the x axis:
To reflect a graph on the x-axis we do [tex]y = -f(x)[/tex] Then [tex]f (x) = -(x-2) ^ 2[/tex]
3) Stretch according to factor 2.
For this we do [tex]y = 2f(x)[/tex]
Then we have [tex]f(x) = -2 (x-2) ^ 2[/tex]
4) Move up the graph in two units:
We do [tex]y = f(x) +2[/tex]
Then [tex]y = -2(x-2) ^ 2 +2.[/tex]
These steps coincide with those listed in the last option. Therefore the correct option is the last one.
"Translate 2 units on the right, reflect on the x-axis, stretch according to the factor 2 and translate 2 units"
