#y=2(x+3)^2+1# is a quadratic equation in vertex form. It can be converted into standard form by doing the following:
Remove the parentheses and exponent by simplifying #(x+3)^2#, which is a sum of squares.
#a^2+b^2=a^2+2ab+b^2#, where #a=x, and b=3#.
#color(blue)((x+3)^2=x^2+2*x*3+3^2)#
Simplify.
#color(blue)((x^2+6x+9)#
Rewrite the equation, substituting #color(blue)((x^2+6x+9))# for #(x+3)^2#.
#y=2color(blue)((x^2+6x+9))+1#
Distribute the #color(red)2#.
#y=color(red)2*x^2+6x*color(red)2+9*color(red)2+1#
Simplify.
#y=color(purple)(2x^2+12x+18)+1#
Simplify.
#color(purple)(y=2x^2+12x+19)#
