University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

453

Pages:

5
Author:

Zander Booth

Name ________________________ Date ____ Analyzing Graphs of Polynomial Functions 4.8 I Essential Question How many turning points can the graph of a polynomial function have? EXPLORATION: Approximating Turning Points Work with a partner. Match each polynomial function with its graph. � your reasoning. Then use a graphing calculator to approximate the coordinates of the turning points of the graph of the function. Round your answers to the nearest hundredth. \tcJ-� rJ..u:;� a. G f(x) = 2x2 + 3x - 4 b. f(x) �\ . t. 1 x2 J+ 3x + 2 A. c. -4 -6 2 3 ·-6 6 -6 6 -7 6 F. / -6 6 -2 4 -6 6 -4 Name ------------------------- Date ____ Notetaking with Vocabula Core Concepts Zeros, Factors, Solutions, and Intercepts Let f (x) = an xn + an _1xn -l + • • · + a1 x + a0 be a polynomial function. The following statements are equivalent. f' t _Y} c * Zero: k is a zero of the polynomial functionf / Factor: (x - �is a factor of the polynomial vvN" �� lA 0.1d ; Y\1·I! (t:."--• l :::- o Cjj �1� -l ) f(x). Solution: k is a solution (or root) of the polynomial equation :: O f(x) = 0. -\-t) '1\c)'i'5 -lie x-lntercept: If k is a real number, then k is an x-intercept of the graph of the polynomial function/ The graph of/passes through )<.-0\ .> 0, then/has at least one real zero between a and b. (�o\ v1t�O;�') N��s� 'f'°''f:t) local maximum �� • local minimum ..ea,..e:.Jw,t., ��: :�:J,....,._ZW!.llf* 191111&;, Turning Points of Polynomial Functions 1. The graph of every polynomial function of degree n has at most n - 1 turning points. + 2. If a polynomial function has n distinct real zeros, then its graph has exactly n - 1 turning points. Notes: ' 'I:>< ·y ;_ ?2- \ I ! t11f'I'� ro, y� • � 7, ?<. 3, \� f'� ·")Oi'i\,\s \ i�<� 'f'·� ?) -\v!-v Name_________________________ Date ____ Notetaking with Vocabulary (continued) J. d e�< '2-_2. �- 0 X"- � 2. X :_ .Ji, A$(.. De. .t(I --� L �� ' <7f,, b �tvvtt V\ 5. f(x) = x4 - 29x2 + 100 6.g(x) = -½x3 + x2 -1 �"'" ' "' Name ___________________-=----, �r Notetaking with Vocabulary (continued) :,;,- Extra Practice ()'I--� tf\_,.'fe.. ?\/I ,it. -t· z, In Exercises 1-6, graph the function. Identify the x-lntercep�, and the points where the local m ximums and local minimums occur. Determine the intervals for which th-;function is increasin or decreasin . Determine whether the function is even, odd, or neither. �_ t_ "" ,. /"I f)O i<'\ rJ' 3. h(x) I =p�- x l 2 ___. F' -13x - 3 � -1�1: - �e,._r;:ro{� +.r-y I p i - s y (� ;\.(), � YL, J..�-'-, "1 � l \ h � p ol'1 i) � 5} O ,- I .p.�fl..cA � fa,c1t'($ I I ( flti+ t�C..-\-?Yf�·, -I -· (w l___: l , "rt, y\. - :: J_ +)_ lvo ..... • (,,\ s " 1 ,. �l ) I �0 • • l../) - -2 .- blt C vt d1t1h Fo , ,1'\ µ, I � ��ei 1M) 1 .t j (.. �( �1. �- L-/ ( I 'l (• 1 "1 '·1•;•-• .'�~- ., --,�..,• ••�..,,.•-.-,,,,.,u,.., .,.,....,.. �•Iii;-'""..,,, • 1((') " '""' - :: '1 .fr;:; _ 4-(t:2.vS J-::',.. �- ,, ' ( t. (A s ; �·"':, \1�r )( L �t,G, I f\,\Or-t. )<' -\'W1v\ > 7-� - �. .r .�,-c........,.._...... -� 2... J Dec..rt�.,tr� t"") -1.b\ L -X. '- � be,-\-WUI'\ �!-{.�'