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.
(10 points)
negative
positiv

1 answer

To determine whether the first term of the cubic polynomial is positive or negative based on the end behavior of the graph, you can observe the directions in which the graph approaches as you move towards the extreme left and extreme right.

If the graph falls to the left (going downwards as you move towards negative infinity) and rises to the right (going upwards as you move towards positive infinity), this indicates that the leading coefficient of the polynomial is positive, because a positive leading coefficient will result in a graph that continuously increases in the positive direction.

Conversely, if the graph rises to the left and falls to the right, this indicates that the leading coefficient is negative, as a negative leading coefficient will cause the graph to decrease as you move toward positive infinity.

In summary, if the graph shows a downward trend on the left and an upward trend on the right, the first term of the equation is negative.