The graph of a polynomial function has four turning points. what is the least possible degree of this polynomial.
The minimum degree of a polynomial with 4 turning points is 5.
The number of turning points in a graph of a polynomial function can be determined by its degree. Each turning point represents a change in direction of the function, meaning that the degree of the polynomial must be at least one more than the number of turning points.
Since you mentioned that the graph has four turning points, the least possible degree of this polynomial would be 5. This is because a polynomial of degree 4 would have at most three turning points, but a polynomial of degree 5 can have up to four.
To determine the least possible degree of a polynomial with four turning points, we need to consider the relationship between the degree of a polynomial and the number of turning points it can have.
The degree of a polynomial is determined by the highest exponent of the variable in the polynomial expression. For example, a polynomial with the highest exponent of 2 has a degree of 2, and a polynomial with the highest exponent of 3 has a degree of 3.
Now, let's look at the relationship between the degree of a polynomial and the number of turning points:
1. A polynomial of degree 0 (constant) has no turning points.
2. A polynomial of degree 1 (linear) has exactly one turning point.
3. A polynomial of degree 2 (quadratic) can have at most one turning point.
4. A polynomial of degree 3 (cubic) can have at most two turning points.
5. A polynomial of degree 4 or higher can have at least three turning points.
Based on this relationship, we can conclude that the least possible degree of a polynomial with four turning points is 4.