Question

-4x^2-12x+1 find the standard form

Answer 1

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.