Respuesta :
Answer:
The new function is [tex]f(x)=(x+7)^2-47[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=x^2+22x+58[/tex]
[tex]f(x)=(x^2+22x)+58[/tex]
To find the vertex from add and subtract [tex](-\frac{b}{2a})^2[/tex] in the parenthesis.
[tex](-\frac{b}{2a})^2=(-\frac{22}{2(1)})^2=11^2[/tex]
[tex]f(x)=(x^2+22x+11^2-11^2)+58[/tex]
[tex]f(x)=(x^2+22x+11^2)-121+58[/tex]
[tex]f(x)=(x+11)^2-63[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
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.
[tex](x,y)\rightarrow (x+4,y+16)[/tex]
[tex](-11,-63)\rightarrow (-11+4,-63+16)=(-7,-47)[/tex]
The vertex of new function is (-7.-47). So the new function is
[tex]f(x)=(x+7)^2-47[/tex]
