Question

Use transformations of the graph of f(x)=x^2 to determine the graph of the given function. h(x)= -(x+4)^2

Answer 1

Given:

`f(x)=x^2`

To determine the graph of the given function f(x) using transformations:

`h(x)=-(x+4)^2`

Since the function f(x) is an upward parabola, the function h(x) is in negative so the function h(x) is drawn a downward parabola.

Also the graph h(x) is shifted 4 units to the left since the graph is adjusted +4 units.

The graph of f(x) is drawn as:

Now, this graph is shifted 4 units to the left and drawn taking reflection along x-axis and is drawn a downward parabola, that is,

This is the graph of h(x) .