Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = - 5 \left( x ^ { 2 } - 3 \right) ( x - 2 ) ^ { 2 }$$
A) falls to the left and falls to the right
B) falls to the left and rises to the right
C) rises to the left and rises to the right
D) rises to the left and falls to the right

Question

Quizplus · Accepted Answer

The leading term of the polynomial, when expanded, will have a negative coefficient (due to the -5) and an even degree (since $x^2$ and $(x-2)^2$ are both squared terms, making the highest degree term $x^4$). Therefore, the end behavior will be that the graph falls to the left and falls to the right, as negative leading coefficients with even degrees result in both ends of the graph pointing downwards.

Use the Leading Coefficient Test to Determine the End Behavior f(x)=−5(x2−3)(x−2)2f ( x ) = - 5 \left( x ^ { 2 } - 3 \right) ( x - 2 ) ^ { 2 }f(x)=−5(x2−3)(x−2)2

Use the Leading Coefficient Test to Determine the End Behavior $f ( x ) = - 5 \left( x ^ { 2 } - 3 \right) ( x - 2 ) ^ { 2 }$