Question

on core algebra i b - cr
the graph of the function ( f(x)=(x + 2)(x + 6) ) is shown below.
which statement about the function is true?
( \bigcirc ) the function is positive for all real values of ( x ) where ( x > - 4 ).
( \bigcirc ) the function is negative for all real values of ( x ) where ( - 6 < x < - 2 ).
( \bigcirc ) the function is positive for all real values of ( x ) where ( x < - 6 ) or ( x > - 3 ).
( \bigcirc ) the function is negative for all real values of ( x ) where ( x < - 2 ).

Explanation:

Step1: Find roots of the function

Set $f(x)=(x+2)(x+6)=0$, solve for $x$: $x=-6$ and $x=-2$.

Step2: Analyze parabola direction

The coefficient of $x^2$ is $1>0$, so parabola opens upward.

Step3: Determine sign intervals

• For $x < -6$: $f(x)>0$
• For $-6 < x < -2$: $f(x)<0$
• For $x > -2$: $f(x)>0$

Step4: Match with options

Only the statement "$-6 < x < -2$ gives negative $f(x)$" is true.

Answer:

B. The function is negative for all real values of x where $-6 < x < -2$.