Question

Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)?

Answer 1

4th graph

Explanation:

Answer 2

we know that

The equation of a vertical parabola in vertex form is equal to

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

where

(h,k) is the vertex

if
`a>0` ------> the parabola open upward ( the vertex is a minimum)

if
`a<0` ------> the parabola open downward ( the vertex is a maximum)

in this problem we have

`g(x)=x^(2)+2x-1`

convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

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

Complete the square. Remember to balance the equation by adding the same constants to each side

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

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

Rewrite as perfect squares

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

`g(x)=(x+1)^(2)-2` --------> equation in vertex form

the vertex is the point
`(-1,-2)`----> is a minimum (parabola open upward)

using a graphing tool

see the attached figure