Question

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6? left 1 unit, up 5 units right 1 unit, up 5 units left 2 units, up 2 units right 2 units, up 2 units

Answer 1

1. Shift left by 1 unit
2. Shift up by 5 units

Explanation:

In order to answer this question first we have to convert g(x) into vertex form.

`g(x)=x^(2)+2x+6\\g(x)=x^(2)+2(x)(1)+(1)^(2)+5\\g(x)=(x+1)^(2)+5`

Now from this form we can visualize the transformations made to f(x) to get the graph of g(x).

Addition of 2 in x means that graph of f(x) = x2 is shifted 1 unit to left to get (x + 1)² .

Addition of 5 in the function value indicates that the graph is shifted 5 units up.

So the changes which have been made to f(x) in order to get g(x) are:

1. Shift left by 1 unit
2. Shift up by 5 units