Solving Quadratics by Factoring and Taking Square Roots Worksheet

Transcription

1 Algebra and 10.4 Part 3 Worksheet Name: Hour: Solving Quadratics by Factoring and Taking Square Roots Worksheet 1. Match each graph n,ith its function. A. ftx) =.v2 I B. AO x2 A- 4 C. Pa') = x2 + 2 a D. fix) = 3x2 5 E. f(x) = 3x2 + 8 E f(x) = of a, e b.-- in/hat Veict liql 1-1(fh -t- 1 A bungee jumper leaves from a platform 256 ft above the ground. Write a quadratic function that gives the jumper's height h in feet after t secon s. Then graph the function. o/ 2.$6) h LT-0 CI hit -Fd What is the original height of the jumper? II d5.6 JI What will the jumper's height be after 1 second?, 16(i) a L6e0 What will the jumper s height be after 3 seconds? Li I') How far will the jumper have fallen after 3 seconds?.256 How long before the jumper would hit the ground if she was not attached to a bungee cord? o -&. St,c,s( What values make sense for the domain? What values make sense for the range? How far has the jumper fallen from time t= 0 to t=1? Does the jumper fall the same distance from time! = 1 to t= 2 as she does from time t = 0 to t= 1? Show work to support your answer. NO) -rails 1.14f

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3 Algebra and 10.4 Part 4 Worksheet Name: 10.3 and 10.4 Word Problems Worksheet Hour: 1. Suppose a person is riding in a hot-air balloon, 144 feet above the ground. He drops an apple. The height of the apple above the ground is given by the formula h =-16t , where h is height in feet and t is time in seconds. a. Graph the functio ti. b. What is the original height of the apple? h -16(c) lo-n c. What will the height of the apple be after 4 seconds? = 1161 on 4-he row d. How far will the apple have fallen after 4 seconds?,e. How long after the apple is dropped will it hit the ground? h 4- lq-11- /6t :7110/ 3sec 61? f. What values make sense for the domain? -11The ('Se c) g. What values make sense for the range? Aezyht ge.,e0 1,-ttt h. How far has the apple fallen from time t = 0 to t = 1? ill= IL/Li liit It =-(1 i. Does the apple' fall the same distance from time t = 1 to t = 2 as it does from time t = 0 to t = 1? Show work to support your answer. koae r- to 2AID s-ec. 7

4 2. Suppose you have a can of paint that will cover 400 ft2. re a. Find the radius of the largest circle you can paint. Round to the nearest tenth of a foot. oo = 7r rrr b. Suppose you hay twocans of paint, which will cover a total of 800 ft2. Find the radius of the largest circle you can paint: Round to the nearest tenth of a foot. Soo A pi. qr c. Does the radius of the circle double when the amount of paint doubles? Explain. no) a.0 d o cth 4-/ c1h& 4, 0a2,0 cc? II) tlo.6poaft2 c c.rns) b141- rad! OS 414 hog _6) c 3. Suppose a squirrel is in a tree 24 ft above the ground. She drops an acorn. Y01,1 vivo an ojecti b =ID a. Write a quadratic function for this situation. Then graph the function. h -I.6t bt 2 = What is a reasonable domain and range for the function? o 4 + S I,.1 scc.s-. 11= C1+2 II l.t n41cs veloci MMINIIIMINIMIMM MMETIMMIMMIIIIIIIM MMMIIIIMEIMIIMM pummummummum 4 CS M MINIIIII MMIMIIIIMIMIIIIIII = MIIMIIIII 11;1% 4. Solve each equation by finding square roots. a. 3d 1 = d1 0 _3 3 b. 7h =1.24 7h2 7 ff i 1/67C--' 0 1 y

5 Arect of a -1-rt4hjle )-) S. Find the value of h for each triangle. If necessary, round to the nearest tenth. a. b. 2 = trro- 6.3f 6. The sides of a square are all increaseciby 3 cm. The area of the new square is 64 cm2. Find the length of a side of the original square. A X4-3 rettç a.quar,' S2-64 X+3)(1k+3) LL X 2 6X You are building a rectangular wading pool. You want the area of the bottom to be 90 ft2. You want the length of the pool to be 3 ft longer than twice its width. What will the dimensions of the pool be? tai Area_ Df a recfan e A= bid W 'O gow (Lu4-3) Lu+ ig -0 ) 90= J4-3W If ) O +31,0 (w.-1-ig)(0' 5 8. The product of two consecutive numbers is 14 less than 1 times the smaller number. Find each number. X = small el- 4p-1) 1X!+ ibx-111- bi et 4 xi-lip-14 =0 x =0 9. Solve x2 = x and x = x by factoring. What number is a solution to both equations? X X

6 10. Suppose you throw a baseball into the air with an initial upward velocity of 29 ft/s and an initial height of 6 ft. The formula h = 16t 2 +29f + 6 gives the ball's height h in feet at time t in seconds. a. The ball's height h is 0 when it is on the ground. Find the number of seconds that pass before the ball lands by solving 0 16t2 + 29f + 6 mt2 #3..a-3I+4 b 11 (4k O z b. Graph the related function for the equation in art (0. Use your graph to estimate the maximum height of the ball. 01(-1(0 MAX Suppose the area of the sail A HO X (n+a) Ho= xx Ac1(. 70GA5)4- lq 1 -R V[.9) lqi shown in file photo is 110 ft2. Find the dimensions 0 x +10( ID Of4 ) X 10 c,?)(-q z 12. A square table has an area of 49 ft2. Find the dimensions of the table. of the sail Solve the cubic equation: x3 10x2 +24x = X it X 7;4 ( L)CX y OX 4;,V71) X 14. You are building a rectangular patio with two rectangular openings for gardens. You have 124. one-foot-square paving stones. Using the diagram below, what value of x would allow you to use all of the stones? Arm 9. A-ect Area a small Rec-t- X Xa 4-1(,X V-,Y "I" I 6 (114--/6)(x_v) /41

7 10.3 and 10.4 Part5 Wors Problems Read each problem carefully and solve-by factoring or taking square roots. 1. Find the x-intercept(s) and y-intercept(s) of the related function: 2x2 + 6x = 20. Then determine if the graph of the related function would open up or down. 16. Set up a quadratic equation and solve it to find the side of a square with an area of 90 ft2. If necessary, round to the nearest tenth. '61 fr 2. A rectangular box has volume 280 in3. Its dimensions are 4 in. x (n + 2) in. x (n + 5) in. Find n. Use the formula V =1-wh 0-1 So 014 dvii-/-5 7 h.-1-7o h-q --pi+ / h 0 71 (hfiz)(11

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9 Hour: Name: Solve by completing the square. 1. x2 4x=5 x 2 4/1,, 4 _ q X2 - U. e Li 7.: 9 (x a)2 = OTI X a ±3 Solving Quadratics by Completing the Square (10.5 Part A) ftett 11,X24. ba' c 2. x2 +10x = 21 2 add (13-)a boi-h sides IOX (4) A2 -I- ox.4- a fochr r bah sides remember + ) X -2-3 Solve 2. e 4- a 4- ; -r 1F-1- X 1 = X = -3 Solve by completing the square. 3. x2 +6x-91=0 x 2 4-6x 91 x 6X1 11 (A#3)`' /Da

10 Solve each equation by completing the square. 5. x2 12x = 0 X 2 * - z- i/5 X 2-102X 1-Pce *5 36 X 2 / 2X1-3t' I x-6 9 x-4 7- = /5 Al z x2 2x = 48( r 41+ x'-.2x4- q9 ± 7 6. x2 4x = 60 etlf X;2 141 'Hi 6 tt _ g x--014 A.-42= -4? I x :4 8. x2 6x 16 = 0 "Y 4-) cz5 --3) X -3 = _3 10. x2-16x+ 28 = 0

11 Hour: w heti b IS Name: Solve by completing the square. Solving Quadratics by Completing the Square (10.5 Part B) 1. x2 6x =- 0 x2 3x =18 X Solve by completing the square. 3. x2 +4x+4=0 X 4. x2 x-2=0

12 Solve each equation by completing the square. 6. x2 +5x = x2 4x.= 8. x2 +4x-12 =0 9. x2 +11x+10=0 10. x2 +2x =15

13 Hour: 0.-=-1 divide by a- ic pc ' hie je-1 sirwler Name: coernci&74 Solve each equation by completing the square. Solving Quadratics by Completing the Square (10.5 Part C) 1. 2x2 +8x =10 X LIX =.5 -- x`l 4-11X 4-h-: 5 'F x2 +12x =32 -a a z VCX+ 3) FT.7- O 1-2)a- =VT k-3 12_( x x2 +5=10x. A2+/ =.2X X2 -,7X+Lt # =0 li" (x -1) X 4-3 =5, TX r: 4. 4x2 12x = 40 A2 3)( = 10 x 2-3X I-012 = A 2-3x q ^ X -.;2 5. 2x2 16x =730 P-IX x 2-41/ 4--tt 11 (x x2 +6x 9 = 0 3 A24-2x-3 0 X2 4-2) 3 x4_1 =-11y- X- 111 = 1, A/ q-= ( 3 I X+ t -2_ -1 z-

14 Solve each equation by completing the square. 7. 2x2 16x + 7 = Xc2 /bx S'Af 7 +Ik x2 -?x.+11, = 9 (x 4) X.-LI 3 X± =3) X I -7 X / 9. Suppose you wish to section off a soccer field as shown in the diagram below. If the area of the field is 450 yd2, fmd the value of x. Area c4 RecfAhsie Az base x o X X 10 ID.2 0 ) X e4- is)2.25-f225 r A rectangle has a width of x. Its length is 10 feet longer than twice the width. Find the dimensions if its area is 28 ft2. A I ac4t21 4-X -Ho /4 (x+.20)(x -1-Q49),VC ,10A f100 c2x -2 boa so X c2 4-3oX 4-30X+ 8. 3x2 +30x = OX X z + tox -1-d5 (x 4-5)2 X + 5 X +5 q 9 X =

15 Hour: Name: Solving Quadratics by Using the Quadratic Formula (10.6) Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth. 1. x2 4x-96 =0 g 2. x2 36 = 0 6 ) X2 +8x+5=0 4. 4x2 12x 91= 0 &.5 5. x2 x = x2 =56 02)

16 Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth. 7. 5x2 =17x x2 3x + 6 =0 Um real sol ( 5x 2-17X-/ 2_ X -4.,3 V 47 x = 17 ± 0814,2'f-6.2C5) g 9. x2 6x = 9 /0 to 6 3 to X )( x2 +6x-8=0 XI-4-3 X x- - 3 ± V 1 X X =3 11. A rectangular painting has dimensions x and x The painting is in a frame 2 in. wide. The total area of the picture and the frame is 144 in2. What are the dimensions of the painting? _ q4- (x+ig)(x4-11)=-gpit x 14-T A ball is thrown upward from the top of a building at a height of 44 ft with an initial upward velocity of 10 ft/s. Use the formula h=-16t 2 +vt +s to find out how long it will take for the ball to hit the ground.