# Question Video: Graphs of Polynomial Functions Mathematics

Determine whether the following statement is true: If the graph of a polynomial does NOT cross the đť‘Ą-axis, then the degree of the polynomial is even.

01:01

### Video Transcript

Determine whether the following statement is true: if the graph of a polynomial does not cross the đť‘Ą-axis, then the degree of the polynomial is even.

A polynomial is either even or itâ€™s odd. If itâ€™s even with a positive leading coefficient, both arrows will go up. If itâ€™s an even polynomial with a negative leading coefficient, both arrows will go down.

Now what happens in between the arrows can vary. If itâ€™s an odd polynomial with a positive leading coefficient, itâ€™ll increase left to right â€” the arrows go in opposite directions â€” and then opposite for a negative leading coefficient for an odd-degree polynomial.

So in order for a graph of a polynomial to not cross the đť‘Ą-axis, the arrows can never go in that direction. So it may be something like this. This means it would be an even-degree polynomial, so this would be a true statement.