Question

How does graph y=-3(x+1)2 -1 transforms from the parent function y=x^2?

Answer 1

Given:

The function is:

`y=-3(x+1)^2-1`

The parent function is:

`y=x^2`

To find:

The transformation of the given function from the parent function.

Solution:

The transformation of a function is given by:

`g(x)=kf(x+a)+b` .... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If k<0, then the graph of f(x) is reflected across the x-axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The given function can be written as is:

`g(x)=-3(x+1)^2-1`

Let the parent function be
`f(x)=x^2`, then

`g(x)=-3f(x+1)-1` ...(ii)

On comparing (i) and (ii), we get

`k=-3,a=1,b=-1`

Therefore, the graph of parent function is stretched vertically by by factor 3 and reflected across the x-axis because
`k=-3`, after that the graph of the function shifts 1 unit left and 1 unit down to get the graph of given function.