Question

Which of the following functions has a graph with a vertex that is a translation 5 units horizontally to the right of the vertex of the graph of y = (x - 1)2+3?

Answer 1

`g(x) = (x-6)^2 +3`

Explanation:

Given

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

Required:

Shift 5 units to the right

f(x) = (x + 2)^2 + 2

The parabola is written as:

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

Where
`(h,k)` is the vertex

Compare
`y = a(x-h) ^2 +k` to
`y = (x - 1)^2 + 3`

The vertex is:

`Vertex =(1,3)`

Shift 5 units to the right

The rule is:

`(x,y) \to (x + 5,y)`

So, we have:

`(1,3) \to (1 + 5,3)`

`(1,3) \to (6,3)`

The new function is:

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

`g(x) = (x-6)^2 +3`