Question

Which statements describe one of the transformations performed on f(x) = x^2

to create g(x) = -(x - 2)^2 +5?
O A. A reflection about the y-axis
B. A translation of 2 units to the left
c. A translation of 5 units up
D. A reflection about the x-axis

Answer 1

The correct options are C and D

C. A translation of 5 units up

D. A reflection about the x-axis

Explanation:

We have been given as function of the graph:

f(x) = x²

Which is transformed into the function

g(x) = -(x-2)² + 5

Consider the graph of y = x²

To convert it into the graph of given transformed function.

First reflect the graph over x-axis, the equation becomes

y = -(x)²

Then translate the graph 2 units to the right

y = -(x - 2)²

Then translate the graph 5 units up.

y = -(x - 2)² + 5

Thus, the correct statements are C and D