NUMBER OF TURNING POINTS OF THE GRAPH OF POLYNOMIAL FUNCTIONS || GRADE 10 MATHEMATICS Q2

Introduction to Turning Points00:00:10

The video introduces the concept of turning points in the graph of a polynomial function. A turning point is defined as a point where the function changes from decreasing to increasing or vice versa. The maximum number of turning points is always less than the degree of the polynomial (n-1).

Example 1: Factored Polynomial00:00:41

The first example demonstrates how to find the degree of a polynomial given in factored form: y = (x+2)²(x+1)³(x-1)⁴(x-2). By adding the exponents of the factors, the degree is found to be 10. Therefore, the maximum number of turning points is 10 - 1 = 9.

Example 2: Expanded Polynomial00:02:08

The second example presents an expanded polynomial: y = -x⁵ + 3x⁴ + x³ - 7x² + 4. The degree of this polynomial is 5 (the highest exponent). Consequently, the maximum number of turning points is 5 - 1 = 4.

Example 3: Simple Monomial00:02:51

This example shows y = x⁴. The degree is 4, so the maximum number of turning points is 4 - 1 = 3.

Example 4: Trinomial00:03:11

The polynomial given is y = x⁴ - 2x² - 15. The degree is 4, leading to a maximum of 4 - 1 = 3 turning points.

Example 5: More Complex Polynomial00:03:31

The final example is y = x⁵ - 5x³ + 4x. The degree is 5, and thus the maximum number of turning points is 5 - 1 = 4.

Conclusion00:03:54

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