Respuesta :
The vertex form of the new function is [tex]\rm (x+7)^2 -47[/tex].
Given
The function [tex]\rm f(x) = x^2 + 22x + 58[/tex] is translated 4 units to the right and 16 units up.
What is the vertex form of function?
The vertex of a parabola is the point at which the parabola passes through its axis of symmetry.
The standard equation which represents the vertex form of the function is;
[tex]\rm f(x) = (x - h)^2 + k[/tex]
Where h and k are vertexes of the given parabola.
The new function after translating 4 units to the right and 16 units up is;
[tex]\rm f(x) = x^2+22x+58\\\\f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2\\\\\f(x) = x^2+22x+(11)^2 +58-(11)^2\\\\ f(x) = (x+11)^2+58-121\\\\f(x)=(x+11)^2-63[/tex]
On comparing with the standard equation of vertex of parabola;
h = -11 and k = -63
Then,
The vertex form of the new function is after translated 4 units to the right and 16 units up.
h = -11 + 4 and k = -63+16 = -47
Therefore,
The vertex form of the new function is;
[tex]\rm =(x+7)^2 -47[/tex]
Hence, the vertex form of the new function is [tex]\rm (x+7)^2 -47[/tex].
To know more about the Vertex form click the link given below.
https://brainly.com/question/411998
