Polynomial function:
[size=100][size=150]Polynomial functions are of the form [br][br][math]f\left(x\right)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0[/math][br]where[math]a_n,a_{n-1},...,a_0[/math] are constants, and [math]n[/math] is a positive integer[br][math]a_n\ne0[/math][br]The degree of a polynomial is[math]n[/math] , which is the highest power of [math]x[/math] in the function.[br]They can be categorized into two types: odd power function and even power function. [br][br][br]For your activity, [br][list][*]Use the sliders to change the values of the coefficients and observe how the graph changes.[br][/*][*]Observe the [b]zeros (x-intercepts)[/b], and the [b]end behavior[/b] of the graph.[/*][*]Answer the guiding questions that follow.[br][/*][/list][/size][/size]
Example of even power polynomial function:
[b]Quadratic function, [/b][math]n=2[/math]
QUESTIONS:
[*]What do you notice about the [b]end behavior[/b] of the graph when the leading coefficient is positive? Negative?[br][br][/*][*]How many [b]x-intercepts (zeros)[/b] can the graph have at most?[br][br][/*][*]What generalizations can you make about the graphs of even-degree polynomials?[/*]
Example of Odd Power Polynomial Function:
[b]Cubic function, [/b][math]n=3[/math]
[*][br][/*]
QUESTIONS:
[*]What do you observe about the [b]end behavior[/b] of the graph when the leading coefficient is positive? Negative?[br][br][/*][*]How many [b]x-intercepts (zeros)[/b] can the graph have at most?[br][br][/*][*]What generalizations can you make about the graphs of odd-degree polynomials?[br][/*]