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

2 Answers

2 votes

Answer:

4th graph

Explanation:

User Cansik
by
6.6k points
4 votes

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

Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)?-example-1
User Jzheaux
by
6.6k points