Transform f(x)=(x+3)(-x-4) to Standard Polynomial Form

To find the standard form of the given quadratic function $f(x) = (x+3)(-x-4)$, we will expand it using the distributive property.

Step 1: Expand the product.
Using the distributive property (or FOIL method):

$f(x) = (x+3)(-x-4)$

Apply distribution:
First: $x \cdot -x = -x^2$
Outside: $x \cdot -4 = -4x$
Inside: $3 \cdot -x = -3x$
Last: $3 \cdot -4 = -12$

Step 2: Combine all terms together:

$f(x) = -x^2 - 4x - 3x - 12$

Step 3: Simplify by combining like terms:
Combine the $x$ terms:

$f(x) = -x^2 - 7x - 12$

Therefore, the standard representation of the function is $f(x) = -x^2 - 7x - 12$.

The correct choice from the given options is choice 4.

$f(x)=-x^2-7x-12$