Question

Given the graph of a polynomial function, determine the minimum possible degree, the zeros and if the multiplicity of the zeros is even or odd. Assume the end behavior and all turning points are represented on the graph. གནད་ a. Determine the minimum degree of the polynomial based on the number of turning points. b. Approximate the real zeros of the function, and determine if their multiplicity is odd or even O a. Minimum degree 4 b. -4 (even multiplicity), -2 (even multiplicity), 3 (odd multiplicity) O a. Minimum degree 3 b. -4 (odd multiplicity), -2 (odd multiplicity), 3 (even multiplicity) O a. Minimum degree 4 b. -4 (odd multiplicity), -2 (odd multiplicity), 3 (even multiplicity) O a. Minimum degree 3 b.-4.-2, and 3 (each with odd multiplicity) O None of these

Answer 1

This graph has three x-intercepts: x = –4, -2, and 3. The y-intercept is located at some (0,c)near (0,-2). At x = –4 and x = -2, the graph passes through the axis linearly, suggesting the corresponding factors of the polynomial will be linear. At x = 3, the graph bounces at the intercept, suggesting the corresponding factor of the polynomial will be second degree (quadratic). Together, this gives us
f(x)=K(x+4)(x+2)(x-3)²
Where K is some factor called stretch factor .
Hence the degree of the polynomial is minimum 4
And real zeroes -4(odd multiplicity),-2(odd multiplicity); 3(even multiplicity).