Question

Identify the vertex of y = x^2 + 4x + 5

A. (4,5)
B. (0,0)
C. (-2,9)
D. (-2,1)
Help me plz, and I hope everyone is having a good day aswell

Answer 1

D. (-2,1)

Explanation:

we have

`y=x^2+4x+5`

This is the equation of a vertical parabola open upward The vertex represent a maximum

Convert the quadratic equation in vertex form

`y=a(x-h)^2+k`

where

(h,k) is the vertex

Complete the square

`y=(x^2+4x+2^2)+5-2^2`

`y=(x^2+4x+4)+5-4`

`y=(x^2+4x+4)+1`

Rewrite as perfect squares

`y=(x+2)^2+1`

The vertex is the point (-2,1)