Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = –x2 + 16x – 44?

the graph of f(x) = x2 is widened.
the graph of f(x) = x2 is shifted left 8 units.
the graph of f(x) = x2 is shifted down 44 units.
the graph of f(x) = x2 is reflected over the x-axis.

D.The graph of is reflected over the x- axis.

Step-by-step explanation:

We are given that a graph

Change into graph of

The g(x) can be written as

Now, the function is translated 8 units towards right by the rule of transformation is given by

By using this rule

Now, translated the graph 20 units down by the rule of transformation is given by

By using this rule

When f(x) is reflected over the x- axis then the rule of transformation is given by

Apply this rule then we get

Hence, the graph of is reflected over the x- axis.

Option D is true.