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