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

Answer:

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

Step-by-step 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:

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

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