Answer:
The correct option is D.
Step-by-step explanation:
The parent function is
[tex]y=x^2[/tex]
The transformed function is
[tex]y=-2(x-2)^2+2[/tex] .... (1)
The translation is defined as
[tex]f(x)=k(x+a)^2+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that
[tex]a=-2,b=2,k=-2[/tex]
It means,
a=-2<0 the graph shifts 2 units right.
b=2>0 the graph shifts 2 units up.
k=-2, the graph reflect across the x-axis and stretch by the factor 2.
The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.
