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

2023
Views:

91

Pages:

7
Author:

NRussell

Characteristics of Quadratic Functions Essential Question ________________ What type of symmetry does 2 the graph of f(x) = a(x - h) + k have and how can you describe this symmetry? a EXPLORATION: Parabolas and Symmetry Work with a partner. a. Complete the table. Then use the values in the table to sketch the graph of the function x2 - 2x - 2 f(x) =. ...l 2 ........ -------- _, ,.--. . .... X f(x) ,. -2 I,\ Sf'e ' -1 0 '� -2 I 1 -3. 5 v1f ;< + 5 ) on graph paper. 2 3 -L( -3. J ,.. \ 4 5 , z_ ,) -for how]. P"l'jc:'... :i -- c.Find a vertical line on your graph paper so that when you fold the paper, the left portion of the graph coincides with the right portion of the graph. What is the equation of this line? How does it relate to the vertex? I 0� r"' 6 o t7i , 0 n.\-l-r t I Yl A h 1� V �'(OV\C.. t \..� ) I (,'_)II 2 d.Sbow that the vertex form f X) = � ( X - 2 ) ( • -- :_ ? X, - - l.(x'- - L..\'?c + ]... . \ -2 ---- -i \ "'"- t16" -4 - 2. � 1 I.� - L( l.� - - 4 ) 6x 2 :/ / .,,,,,✓ - - 4 is equivalent to the function given in part (a). (x\{x.\ + (-->\(-:ti ➔ (-iVx'1--\ (-1 { l l t ,_� -4 1- � e,./ +l-r - ± (x -z){x-� - 1-,I f - 2- � -=6 t - -·- --· \ >- ('7--J-'--1) .p. fLl. - ,- 4 L/ b.Use the results in part (a) to identify the vertex of the parabola. O - 6 ----- vr--d v--t s. · 0 + J· i,10'::>e 6',y I .. .. Parabolas and Symmetry • Work with a partner. Repeat Exploration 1 for the function given by 2 f(x) = -1x + 2x + 3 = -2 X f(x) -1 -2� ,fo 0 1 2 3 t-t.I: s.� � - _._ - _.__ 2 -1(x - 3) + 6. 4 5 S,b 11,-b -6'�y -4 ,_'-,_'- 3 _VV � [\ I 11 -27I L- ,_,2 2 4 + 14 16,., Communicate Your Answer 3.What type of symmetry does the graph of the parabola f(x) = a(x - h) + khave and how can you describe this symmet�1) 2 G__:: ) T+ i< ; tk v�rkr�l L--;� jO•') 4.Describe the symmetry ,of each graph. Then use a graphing calculator to verify your answer. a. f(X) = -( X - 2 1) + 4 b. \Je-, ky { I ) ti) d. /(x) 0 = 1(x + 2)2 -t- (? \J e rk,x ( ,,i_) o ') G_0 f(x) = (x + 1) 2 - 2 \Je,,Ae� {- l J -2,J c. f(x) = -2x 2 + 3 � t1"-e.x__(o J �") ( x+o")'- c_0 ( 'J.; I) G V e. f(x) = 2(x - 3) 2 + 1 \J t. r+e � f. f(x) = ,- \ - _J_' � -=6 6 -4 , 3(x - s)2 +2 V � rk. 't< - ( s1 2-') � 6x Notetaking with Vocabulary \)e./� )< \-o ( f/\ r1 , ['X :: (X - "L + ,-.. &,, In your own words, write the meaning of each vocabulary term. axis of symmetry "' lr< V -1-vh- , � l i -t:.· 4- !"\. «-f 1, L I ·/. l / t(., r•'� 1-f.HCt ; "'' nA 1 •1 standard form minimum value maximum value +- c�+-'> + Is ft-._e__ �- pe. / ovvr:. St fl/Jrc>1bo{�_ intercept form I poi vi-+ r. nc 2- -+""i"(' {r?:, ! ___ I,.,\ /- O r1 b r- \r - - ) 3. - 1, 1--+--+-1--+--+--+-+--+----+-----< � X - - 2