Answer:
Option C is correct.
Step-by-step explanation:
The given function f(x) is:
f(x) = x^2 + 22x + 58
To find the vertex find
and add and subtract it from both sides of the given function
b= 22, a= 1
Putting values:
![(\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B-b%7D%7B2a%7D%20%29%5E2%20%3D%20%28%5Cfrac%7B-22%7D%7B2%281%29%7D%29%5E2%5C%5C%3D%28%5Cfrac%7B-22%7D%7B2%7D%29%5E2%5C%5C%3D%20%28-11%29%5E2%5C%5C%3D11%5E2)
Adding (11)^2 on both sides
f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2
f(x) = x^2+22x+(11)^2 +58-(11)^2
a^2 +2ab+b^2 = (a+b)^2 Using this formula:
f(x)=(x+11)^2+58-121
f(x)=(x+11)^2-63
The vertex of the given function is (-11,-63)
The function is translated 4 units to right and 16 units up
The vertex of new function will be:
(x+4,y+16) => (-11+4,-63+16)
=> (-7,-47)
So, the vertex of new function is (-7,-47)
The function will be
(x+7)^2 -47
So, Option C is correct.