Write an equation for the function that is described by the following characteristics. The shape of f(x) = x^2 but moved nine units down, four units to the left, and then reflected over the x-axis.

Answer 1

Based on the order you listed your transformations of f(x) = x²:

9 down....subtract 9 from the original function

x²-9

4 to the left...add 4 to the inside of the function to move it sideways...leave the minus 9 on the end

(x+4)²-9

after that, reflect it over the x-axis. This results in all y values becoming the oppposite of what they were, which is like putting a negative on the entire function to change the sign of all y-values

-[(x+4)²-9]

which is the same as -(x+4)²+9....the final answer