Question

A polynomial function with an odd degree and a negative leading coefficient extends from the _________ quadrant to the __________ quadrant.

Accepted Answer

The odd degree polynomial function, whose leading coefficient is negative, extends from quadrant 2 to quadrant 4.
Consider as example the following odd degree polynomial function, having negative leading coefficient, such that:
f(x) = -x^3 + x^2 - x + 1 
The graph of the polynomial is sketched below, such that:

You should notice that the graph descends from the quadrant 2 (where it starts) to the quadrant 4 (where it ends).

Answer

A polynomial function with an odd degree and a  negative leading coefficient extends from the _second__ quadrant to the  _fourth_ quadrant.
If you draw a couple examples of this or (if you can use a graphing calculator, let it do the work.)
Examples of this would be -3x^3  or -52x^57  or as it's most basic -x or -x^3. (^ means to the power that bollows it, so this last one is "negative x to the third power)

Math

A polynomial function with an odd degree and a negative leading coefficient extends from the _ quadrant to the __ quadrant.

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