Answer:
option (c) is correct.
The vertex form of given function [tex]h(x)=7+10x+x^2[/tex] is [tex]h(x)=(x+5)^2-18[/tex]
Step-by-step explanation:
Given : [tex]h(x)=7+10x+x^2[/tex]
We have to write h(x) in vertex form
For a given quadratic function [tex]f(x)=ax^2+bx+c[/tex] the vertex form can be written by completing square in such a way that we get, the equation in the form of [tex]f(x)=a(x-h)^2+k[/tex] , where (h,k) is the vertex.
Consider the given function [tex]h(x)=7+10x+x^2[/tex]
first writing in standard form , we get,
[tex]h(x)=x^2+10x+7[/tex]
Using identity, [tex](a+b)^2=a^2+b^2+2ab[/tex] , we have
x = a , and 2ab = 10x
Comparing , we get, b= 5
we need to add [tex]b^2[/tex] term
So add and subtract 25 in the given function , we get,
[tex]h(x)=x^2+10x+25-25+7[/tex]
Simplify , we get,
[tex]h(x)=(x+5)^2-18[/tex]
Thus, the vertex form of given function [tex]h(x)=7+10x+x^2[/tex] is [tex]h(x)=(x+5)^2-18[/tex]
option (c) is correct.
