Question

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 9x2 – 36x?

The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted right 4 units.
The graph of f(x) = x2 is shifted down 36 units.
The graph of f(x) = x2 is reflected over the x-axis.

Answer 1

Rewrite g(x): g(x) = 9x^2 − 36x = 9(x^2 − 4x) = 9[(x − 2)^2 − 4] = 9(x − 2)^2 − 36.
So f(x)=x^2 is shifted right 2, vertically stretched by 9, and shifted down 36. Therefore the correct choice is: The graph of f(x)=x^2 is shifted down 36 units.