Answer:
The vertex of the graph is (-3, -4).
Step-by-step explanation:
Given quadratic function is,
[tex]y=x^2+6x+5[/tex]
For finding the vertex we need to change the given expression in the form of [tex]y=a(x-h)^2+k[/tex],
For this we must add and subtract the square of the coefficient of middle term,
Since, the half of 6 = 3
Add and subtract the square of 3 in the right side of the equation,
[tex]y=x^2+6x+5+9-9[/tex]
[tex]y=(x^2+6x+9)+5-9[/tex]
[tex]y=(x+3)^2-4[/tex]
We know that,
For the function [tex]y=a(x-h)^2+k[/tex]
Vertex = (h,k)
By comparing,
The vertex of the given function is (-3, -4).
