Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21

Answer:[tex]y=(x+4)^{2}-37[/tex] Step-by-step explanation:we know thatThe equation of a vertical parabola into vertex form is equal to[tex]y=a(x-h)^{2}+k[/tex]where(h,k) is the vertex of the parabolaif a> 0 then the parabola open upward (vertex is a minimum)if a< 0 then the parabola open downward (vertex is a maximum)In this problem we have[tex]y=x^{2}+8x-21[/tex]Convert to vertex formComplete the square [tex]y+21=x^{2}+8x[/tex][tex]y+21+16=(x^{2}+8x+16)[/tex][tex]y+37=(x^{2}+8x+16)[/tex][tex]y+37=(x+4)^{2}[/tex][tex]y=(x+4)^{2}-37[/tex] --------> equation in vertex formThe vertex is the point [tex](-4,-37)[/tex]the parabola open upward (vertex is a minimum)