Question

To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 5 units and 9 units.

Answer 1

To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 ✔ right
5 units and ✔ down 9 units.

Answer 2

The graph of f(x) shifts 5 units right and 9 units down to graph g(x).

Explanation:

The general form of the parabola is

`h(x)=a(x-h)^2+k`

Where, (h,k) is the vertex of the parabola and a is stretch factor.

The parent function is

`f(x)=x^2`

The vertex of the parabola is (0,0).

The given function is

`g(x)=(x-5)^2-9`

The vertex of the parabola is (5,-9).

The vertex of the parabola shifts from (0,0) to (5,-9), therefore the graph of f(x) shifts 5 units right and 9 units down to graph g(x).