Question

Functions f(x) and g(x) are shown:

f(x) = x2
g(x) = x2 − 12x + 36

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Left by 18 units
Right by 18 units
Left by 6 units
Right by 6 units

Answer 1

D is correct

Explanation:

I took the test

Answer 2

Shifted right 6 units.

Explanation:

`g` can be written as a squared binomial since it is of the form:

`x^2+2ax+a^2` which can be written as
`(x+a)^2`.

When comparing the expression to the trinomial just mentioned it should be noted that
`a` is -6. So
`g` can be written as:
`g(x)=(x-6)^2`.

Note: Vertex form of a quadratic is
`y=a(x-h)^2+k` where (h,k) is the vertex.

The vertex of the parent is (0,0) and the vertex of
`g` is (6,0). So the parent has shifted right 6 units to get to where
`g` is located.