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? (x – 11)2 + 58 (x + 22)2 – 121 (x + 7)2 – 47 (x – 15)2 + 94

The vertex form of the new function is [tex]\rm (x+7)^2 -47[/tex].GivenThe 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 = -63Then,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 = -47Therefore,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.