Question

The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?

Answer 1

The answer to this equation is C.
C. (x + 7)2 – 47

Answer 2

The new function is
`f(x)=(x+7)^2-47`.

Explanation:

The given function is

`f(x)=x^2+22x+58`

`f(x)=(x^2+22x)+58`

To find the vertex from add and subtract
`(-(b)/(2a))^2` in the parenthesis.

`(-(b)/(2a))^2=(-(22)/(2(1)))^2=11^2`

`f(x)=(x^2+22x+11^2-11^2)+58`

`f(x)=(x^2+22x+11^2)-121+58`

`f(x)=(x+11)^2-63`
`[\because (a+b)^2=a^2+2ab+b^2]`

The vertex of the given function is (-11,-63).

It is given that the function f(x) is translated 4 units to the right and 16 units up.

`(x,y)\rightarrow (x+4,y+16)`

`(-11,-63)\rightarrow (-11+4,-63+16)=(-7,-47)`

The vertex of new function is (-7.-47). So the new function is

`f(x)=(x+7)^2-47`