Question

What is the new function’s equation (green)?

Answer 1

`f(x)=-(x+3)^2`

Explanation:

The parent function is f(x) = x^2.

• This can be reasoned by the fact that this is a postive parabola that is on the origin.

The green function is moved 3 units to the left. This means that the function changes like this:

• 
  `x^(2)` -->
  `(x+3)^2`

The green function is also reflected over the x-axis.

Functions that are reflected over the x-axis take are multiplied by an exterior negative (literally, a negative on the outside)

• Ex; f(x) flipped over x-axis= -f(x)

So, we put a negative on the outside.

`(x+3)^2` -->
`-(x+3)^2`

The function isn't moved up or downwards, so we don't have to add or subtract anything on the outside.

The function is also not stretched or shrunk.

So, the equation of the green function is:

`f(x)=-(x+3)^2`