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

The answer is c

Explanation:

Answer 2

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

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