PLEASEE could someone help me with this and show work

Accepted Solution

Answer:Axis of symmetry: [tex]x=-3[/tex]Vertex: [tex](-3,-5)[/tex] Step-by-step explanation:The given equation is [tex]y=2x^2+12x+13[/tex]We complete the square to get the function in the vertex form.[tex]y=2(x^2+6x)+13[/tex][tex]y=2(x^2+6x+9)-2*9+13[/tex][tex]y=2(x+3)^2-18+13[/tex][tex]y=2(x+3)^2-5[/tex]We compare to [tex]y=a(x-h)^2+k[/tex]We have a=2,h=-3 and k=-5The equation of axis of symmetry is x=hi.e [tex]x=-3[/tex]The coordinate of the vertex is (h,k) i.e [tex](-3,-5)[/tex]