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

we know that

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

where

(h,k) is the vertex

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

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

in this problem we have

convert to vertex form

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

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

Rewrite as perfect squares

--------> equation in vertex form

the vertex is the point ----> is a minimum (parabola open upward)

using a graphing tool

see the attached figure

here

step-by-step explanation:

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.