Question

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

Answer 1

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 $a$ ------> 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

Answer 2

Answer:

the answer is d the last one :)

Step-by-step explanation: