I'd stay this expression is already in standard form, although you could rewrite it as -(-4x^2-12x+1).
You could rewrite -4x^2-12x+1 by completing the square:
-4(x^2 + 3x ) +1 becomes
-4(x^2 + 3x + [3/2]^2 ) - [3/2]^2 + 1, or
-4(x + 3/2)^2 + 1 - 9/4, or
-4(x+3)^2 -5/4 (final form) The graph would be that of a parabola with vertex at (-3, -5/4). This parabola would open down and would be vertically stretched by a factor of 4.