Questions: Polynomial Functions Graphs Apply The image below shows a cubic polynomial. Use the graph to answer the questions. 1.) Is the FIRST term of the graphed equation positive or negative? In a complete sentence on your "work page", explain how to know if the first term of the equation is positive or negative based on the end behavior of the graph.

Solution Steps

Observe the graph of the cubic polynomial. Notice the behavior of the graph as \( x \) approaches positive and negative infinity.

For a cubic polynomial \( ax^3 + bx^2 + cx + d \):

• If the leading coefficient \( a \) is positive, the graph will fall to the left and rise to the right.
• If the leading coefficient \( a \) is negative, the graph will rise to the left and fall to the right.

From the graph:

• As \( x \) approaches negative infinity, the graph rises.
• As \( x \) approaches positive infinity, the graph falls.

This indicates that the leading coefficient \( a \) is negative.

Final Answer