which is the graph of $f(x) = -(x + 3)(x + 1)$?
which is the graph of $f(x) = -(x + 3)(x + 1)$?
Answer
Explanation:
Step1: Find x-intercepts
Set ( f(x) = 0 ), so ( -(x + 3)(x + 1)=0 ). Then ( x + 3 = 0 ) or ( x + 1 = 0 ), giving ( x=-3 ) and ( x=-1 ). The graph should cross the x - axis at ( x=-3 ) and ( x=-1 ).
Step2: Determine parabola direction
The coefficient of ( x^{2} ) (after expanding) is - 1 (since ( -(x + 3)(x + 1)=-(x^{2}+4x + 3)=-x^{2}-4x - 3 )). A negative leading coefficient means the parabola opens downward. Looking at the graphs, the second graph (middle - top) has x - intercepts at ( x=-3 ) and ( x=-1 ) and opens downward.
Answer:
The Middle - Top Graph (the second graph in the top row)