Using the Quadratic Formula

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

2021
Views:

413

Pages:

5
Author:

Cohen Williams

Using the Quadratic Formula be. {--6, W\ d ,t ?I .(. t·· vi.. i V\ > ' • How can you derive a general formula for solving a quadratic equation? l <. 1 Essential Question EXPLORATION: Deriving the Quadratic Formula Work with a partner. Analyze and describe what is done in each step in the development of the Quadratic Formula. Justification Step l., (,; v-e Y\ ax 2 +bx+ c = l = -a 0 ax2 + bx = -c X 2 x + The result is the Quadratic Formula. C + }?__ = ± 2a � ( b a -X ✓ b 2 -4ac 4a2 b .Jb 2 -4ac x=--+---2jaj 2a ✓ 2 -b ± b -4ac X=-----2a -- ... r oll Notetaking with Vocabulary For use after Lesson 3.4 In your own words, write the meaning of each vocabulary term. b,....s-" � Quadratic Formula (!J (ll.,... Let a, b, and c be real numbers such that a -::f:. The solutions of the quadratic equation 2 X 0. -l 'fl..e Sfc.i p, J. h ( J_. Fol M :, - 2a --- I 0 4a� ....- :f� 'lt.._Jc,.. ("� Analyzing the Discriminant of ax � "V'),-J - ....,,,,.,,,.,.\ Value of discriminant Number and type of solutions (r,{ WI + bx + c = 0 2 r+ J b2 1< - 4ac > 0 I' Jo� J b2 - 4ac = 0 b2 /( - 4ac < 0 \l Two real solutions One real solution Two imaginary solutions Twox-intercepts Onex-intercept Nox-intercept Graph of y = ax2 +bx+ c o +- -fl.e.. "'--A. 1 d� �'c._ Extra Practice In Exercises 1-3, solve the equation using the Quadratic Formula. 2 2 1. x - 7 X - 18 = 0 2. w b : -7 '--'L •• \ l -:. - , 't' �;,,<�•�"'--••- •••�J, � i.. -� -�, )1 J(1��-='-(( 'i-1 � 2(( 1 -· / i "" Jiil' LJ. �� -� -7z = -4z2 3. - ,-11 3 + I.{ t, + 1, '1. - t.f c1. ... ;-., +-� b-=--1 • •• i .. t-11:: J -, ') I! "'o • •,-.;-.,.;,._,q-�,�.5tt�,C, h -;,-"( C-;. I ?-( () 0 14,-y � ��"'.,.,.�,��"""'" ,,,.. "(t 7--r \ r----;. ..) - -itril J�'- ¥ -0 © � � � - r.o ... � 7-t • _. � ,.., In Exercisel4-6, find the discrimin3mt of the quadratic equation and describe the number and type of solutions of the equation. 4. b 2 + 34b + 289 = 0 L I� , b-;"711 C ----· c.. J h ..... _ '1 -:..z.�'1 ;. J ( �� ... -¼C L "i(t� --; � 11 ��--_ II S(o 6. ;.. 4q 2 + 1 = 3q -1.i ->ti., ��,._ - 3'i-- t ' --;. u t �)\. .. y ( Ja, -, l Jo s. x 2 = 3 - 8x ...-\ +� x'L.-----+�>< ... ; � o i 'L.- a.., C) (-;1 J'=>trt+12.. v 7b 0 )( 1 ) ·1 -i • (,, �t/if.,,."i.· '2,. _,,,c )(?>, Ji.i� •"'I� "'I w + t � • o·· • /, .,. ,. ' '" • (-'i\ t /7-'i'/ - • "t (·- ) C I \ �/,'-, c.. ::- 3, 'Z.c( l) I c'... •. ( l 7 211:.. f:. 'i)) 7±J't�+-7Z. = 4w - 1 •t.( W f I 7. A a. seball player bits a foul ball straight up in the air from a height of 4 feet offthe ground with an initial velocity 85 feet per second. h ( t) .,.. ... l fo i_ -i- • + VO -f; I 0 Write a quadratic function that represents the height h of the ball t seconds after it hits the bat. + ,fl\.(1- 'f :: "" ,� )l �vt "' t..t h � "'-' 1"5k• -t :.. fi� he,"Sv,+ b. When is the ballf ��ee1ffthe ground? Explain your reasoning. ,. c.r -uo 110= -tbt r�·si- + -t I O 6 :. -· I 6-t-1... + � S' ii .... I O fo ' i�)! v(�� ... 1.1 l 2,( °'.) -�s:tG'i2. - '- 7