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Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those with a negative leading coefficient.

User Tryer
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When the leading coefficient is positive, the polynomial, with a degree of 3, starts in the bottom left quadrant and ends in the top-right quadrant. While for the negative leading coefficient, the curve starts in the top-left quadrant and ends in the bottom-right quadrant

Other features of the polynomial

The end behaviors

Leading coefficient is positive:

  • As x goes to negative infinity, the function approaches negative infinity
  • As x goes to positive infinity, the function approaches positive infinity

Negative Leading Coefficient:

  • As x goes to negative infinity, the function approaches positive infinity
  • As x goes to positive infinity, the function approaches negative infinity

A graph is attached to represent the positive leading coefficient and the negative leading coefficient.

The orange color is the positive leading coefficient while the purple like color is the negative leading coefficient

User David Collins
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