Question

Which function transforms the graph of y= x^2 so that it is first shifted down 4 units and its then reflected across the y- axis?
A. y= -x^2 +4
B. y= -x^2 - 4
C. y= ( -x)^2 -4
D. y= - ( x + 4 )^2

Answer 1

Answer:

Option C. y= ( -x)^2 -4

Step-by-step explanation:

If we have a function $f(x) = ax ^ 2$ and we want to transform it into a function g(x) that is equal to f(x) displaced c units down on the y-axis, then we must do:

$g(x) = f(x) -c$

In this case we want to move the function 4 units down, then:

$g(x) = f(x) -4\\\\g(x) = x ^ 2 -4$

Finally, to reflect the function on the y-axis. must do $y = g(-x)$

Then we have the following function:

$g(-x) = (-x) ^ 2 -4\\\\y = (-x) ^ 2 -4$

The answer is option C