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

Accepted Solution

we know thatThe equation of a vertical parabola in vertex form is equal to[tex]y=a(x-h)^{2}+k[/tex]where(h,k) is the vertexif [tex]a>0[/tex] ------> the parabola open upward ( the vertex is a minimum)if [tex]a<0[/tex] ------> the parabola open downward ( the vertex is a maximum)in this problem we have[tex]g(x)=x^{2}+2x-1[/tex]convert to vertex formGroup terms that contain the same variable, and move the constant to the opposite side of the equation[tex]g(x)+1=x^{2}+2x[/tex]Complete the square. Remember to balance the equation by adding the same constants to each side[tex]g(x)+1+1=x^{2}+2x+1[/tex][tex]g(x)+2=x^{2}+2x+1[/tex]Rewrite as perfect squares[tex]g(x)+2=(x+1)^{2}[/tex][tex]g(x)=(x+1)^{2}-2[/tex] --------> equation in vertex formthe vertex is the point [tex](-1,-2)[/tex]----> is a minimum (parabola open upward)using a graphing toolsee the attached figure