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

The correct option is D.

Step-by-step explanation:

The parent function is

The transformed function is

             .... (1)

The translation is defined as

               .... (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

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.

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!