Polynomial Multiplicity Review Zeros of Polynomial Functions If
- Slides: 23
Polynomial Multiplicity
Review Zeros of Polynomial Functions
If f is a polynomial function, then the values of x for which f(x) is equal to 0 are called the zeros of f. These values of x are the roots, or solutions, of the polynomial equation f(x)=0. Each real root of the polynomial equation appears as an x-intercept of the graph of the polynomial function.
Find all zeros of f(x)= x 3+4 x 2 - 3 x - 12
Example Find all zeros of x 3+2 x 2 - 4 x-8=0
Answer Find all zeros of x 3+2 x 2 - 4 x-8=0 Zeros: x = 2, -2
Multiplicity of x-Intercepts
Multiplicity Video • Watch both!!! Create a table for multiplicity to graph! • Find the zeros, multiplicity, end behavior, and y-intercept to sketch a graph. • https: //www. youtube. com/watch? v=v 3 Yzjt 6 YSY 8 • https: //www. youtube. com/watch? v=Pci. Yb wy. N 8 ZM
Graphing Calculator- Finding the Zeros x 3+2 x 2 - 4 x-8=0 One zero of the function One of the zeros Other zero The other zero The x-intercepts are the zeros of the function. To find the zeros, press 2 nd Trace then #2. The zero -2 has multiplicity of 2.
Example Find the zeros of f(x)=(x- 3)2(x-1)3 and give the multiplicity of each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. Continued on the next slide.
Answer Find the zeros of f(x)=(x- 3)2(x-1)3 and give the multiplicity of each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. Zeros: x=3 multiplicity 2 – touches and turns around x=1 multiplicity 3 – crosses Continued on the next slide.
Example Now sketch this function on your INB. f(x)=(x- 3)2(x-1)3 Remember end behavior!!!
Answer Now sketch this function on your INB. f(x)=(x- 3)2(x-1)3 Remember end behavior!!!
A Strategy for Graphing Polynomial Functions
Example Graph f(x)=x 4 - 4 x 2 using what you have learned in this section.
Answer Graph f(x)=x 4 - 4 x 2 using what you have learned in this section.
Example Graph f(x)=x 3 - 9 x 2 using what you have learned in this section.
Answer Graph f(x)=x 3 - 9 x 2 using what you have learned in this section.
State whether the graph crosses the x-axis, or touches the x-axis and turns around at the zeros of 1, and - 3. f(x)=(x-1)2(x+3)3 (a) (b) (c) (d)
State whether the graph crosses the x-axis, or touches the x-axis and turns around at the zeros of 1, and - 3. f(x)=(x-1)2(x+3)3 (a) (b) (c) (d)