Question

Which steps transform the graph of y = x2 to y = –2(x – 2)2 + 2? (1 point)

A. translate 2 units to the left, translate down 2 units, stretch by the factor 2
B. translate 2 units to the right, translate up 2 units, stretch by the factor 2
C. reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2

Answer 1

y = x^2 to Green

y = –2(x – 2)^2 + 2 Blue

The correct answer is D.

Answer 2

The correct option is D.

Explanation:

The parent function is

`y=x^2`

The transformed function is

`y=-2(x-2)^2+2` .... (1)

The translation is defined as

`f(x)=k(x+a)^2+b` .... (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

`a=-2,b=2,k=-2`

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.