Question

Predict the change from the parent function f(x)=x2 for each function. (Explain how it willlook different or transformed) Also include where the vertex will be for each.

Answer 1

The aprent function is:

$f(x)=x^2$

and the new function is:

$j(x)=-(x+5)^2+2$

This is related as follows:

The new function is relfected about the x axis, then it is translated 5 units to the left and 2 units up.

This is shown in the following graph:

where the red graph is f(x) and the blue one is j(x).

Now, the vertex of the original function is the origin; whereas for the second function is in the point (-5,2).