Polynomial functions have graphs that are smooth and continuous. c) Use your knowledge of quadratic functions to sketch the graph.

Size: px

Start display at page:

Download "Polynomial functions have graphs that are smooth and continuous. c) Use your knowledge of quadratic functions to sketch the graph."

Patience Moody
5 years ago
Views:

1 Math Polyomial fuctios I class work Polyomial fuctios have graphs that are smooth ad cotiuous 1) For the fuctio: y 2 = x 9. a) Write the fuctio i factored form. b) Fid the x-itercepts or real zeros of the fuctio. c) Use your kowledge of quadratic fuctios to sketch the graph. 2 2) For the fuctio: y = 2x 18. a) Write the fuctio i factored form. b) Fid the x-itercepts or real zeros of the fuctio. c) Use your kowledge of quadratic fuctios to sketch the graph. 3) For the fuctio: yy = xx 2 5xx + 6. a) Write the fuctio i factored form. b) Fid the x-itercepts or real zeros of the fuctio. c) Use your kowledge of quadratic fuctios to sketch the graph. 4) For the fuctio: yy = 3xx xx 18. a) Write the fuctio i factored form. b) Fid the x-itercepts or real zeros of the fuctio. c) Use your kowledge of quadratic fuctios to sketch the graph. 5) Summary of observed patters: Commet o degree, leadig coefficiets ad ed behavior 1

2 Writig a polyomial fuctio from its zeros 6) A quadratic fuctio has x-itercepts -3 ad 4. a) Sketch a possible graph (1) With positive ed behavior (2) With egative ed behavior b) Write TWO possible fuctios for each graph; give the degree ad the leadig coefficiet. 7) A polyomial fuctio has x-itercepts -5, -3, ad 2. a) Sketch a possible graph (1) With positive ed behavior (2) With egative ed behavior (2) Write TWO possible fuctios for each graph; give the degree ad the leadig coefficiet. 8) Make up some reasoable values for the x-itercepts ad write possible fuctios for the followig graphs. 2

3 9) Without the calculator, graph a) yy = (xx 3) 2 b) What do you thik the graph of yy = xx(xx 3) 2 will look like? Sketch ad check with the calculator. c) yy = (xx 3) 3 d) What do you thik the graph of yy = xx(xx 3) 3 will look like? Sketch ad check with the calculator. e) Complete the followig table: yy = (xx 3) 2 yy = xx(xx 3) 2 yy = (xx 3) 3 yy = xx(xx 3) 3 Leadig term Degree Ed Behavior Zeros ad multiplicities Behavior at the x- axis 3

4 10) Turig Poits: For each type of fuctio, show some graphs ad commet o the umber of turig poits: a. Liear fuctio b. Quadratic c. Cubic d. Fourth degree e. Fifth degree 11) Summarize properties of graphs of polyomial fuctios (refer to page 189 of the book, 6 th ed.) Complete the followig: The format of a polyomial fuctio is: f(x) = a. Degree: b. Graph c. Maximum umber of turig poits d. At a zero of eve multiplicity e. At a zero of odd multiplicity f. Betwee the zeros g. Ed behavior 4

5 12) Write a polyomial fuctio with give degree, x-itercepts ad a specific y-itercept. 5

6 Math 165 Reviewig Polyomial Fuctios Name Turig poits ad zeros 1) A 4 th degree polyomial has at most turig poits, ad at most real zeros. 2) A th degree polyomial fuctio has at most turig poits, ad at most real zeros. 3) The miimum umber of real zeros of a odd degree polyomial fuctio is 4) The miimum umber of real zeros of a eve degree polyomial fuctio is Ed behavior 5) For ay degree, if 0 a >, the right ed behavior is UP / DOWN 6) For ay degree, if a < 0, the right ed behavior is UP / DOWN 7) Summary for ed behavior Idicate with arrows the possibilities for the ed behavior of Eve degree polyomial fuctio Odd degree polyomial fuctio a > 0 a < 0 Rage 6) If is odd, the rage of the polyomial fuctio of degree is 7) Idicate possibilities for the rage of eve degree polyomial fuctios. Summary for rage 8) Write the possibilities for the rage based o the degree of the polyomial Rage of a eve degree polyomial fuctio Rage of a odd degree polyomial fuctio a > 0 a < 0 Zeros, factors, multiplicity ad behavior at the x-coordiates of the zeros 9) If a polyomial fuctio has a zero of multiplicity 1 at x = b, the the fuctio has a factor ad the graph the x axes at x = 10) If a polyomial fuctio has a zero of odd multiplicity M (M > 1) at x = c, the the fuctio has a factor ad the graph at x = 11) If a polyomial fuctio has a zero of eve multiplicity K at x = d, the the fuctio has a factor ad the graph at x = 6

number in a data set adds (or subtracts) that value to measures of center but does not affect measures of spread.

number in a data set adds (or subtracts) that value to measures of center but does not affect measures of spread. Lesso 3-3 Lesso 3-3 Traslatios of Data Vocabulary ivariat BIG IDEA Addig (or subtractig) the same value to every umber i a data set adds (or subtracts) that value to measures of ceter but does ot affect