NO) Tails 4,4 r ----p h

Transcription

1 Algebra and 10.4 Part 3 Worksheet Name: Hour: Solving Q adratics by Factoring and Taking Square Roots Worksheet 1. Match each grop.1 A.) its function. A. = x2 I B. f(x) = x + 4 D. f(x) = 3x2 5 E. f(x) = 3x2 + 8 C. Px.) = x2 2 CI E Ay) = + 5 CI 7; 1 6 ) b //' 17a Vela. = h-etiht- 2. 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. What is the original height of the jumper? 0 ) h() What will the jumper's height be after 1 second? I ) li )2.1,256 C What will the junk rsheight be after 3 seconds? h u -3) How far will the jumper have fallen after 3 seconds? A 44 How long before the jumper would hit the ground if she was not attached to a bungee cord? = L/- Sc( What values make sense for the domain? What values make sense for the range? D DLL R How far has the jumper fallen from time t = 0 to t= I? 56-2 I/ Does the jumper fall the same distance from time I = 1 to t = 2 as she does from time t = 0 to t = 1? Show work to support your answer. NO) Tails 4,4 r ----p h 110,sces

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3 Algebra and 10.4 Part 4 Worksheet Name: 10.3 and 10.4 Word Problems Worksheet Hour: I. 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 = -16t2 +144, where h is height in feet and t is time in seconds. a. Graph the functio-ri. b. What is the original height of the apple? +7=0: (PI c. What will the height of the apple be after 4 seconds? -E=4: -.1-U LO - lla f4 fdr the L9 1 OWd d. How far will the apple have fallen after 4 seconds? 144 -Ft e. How long after the apple is dropped will it hit the ground? hvo: = -/6 62' Mit "I 4 - f. What values make sense for the domain? -tfiyi e Cse c) g. What values make sense for the range? A efght gee. h. How far has the apple fallen from time t = 0 to t= 1? h /6 0 - I sec 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. so g ino

4 2. Suppose you have a can of paint that will cover 400 ft2. Area, = 70- a. Find the radius of the largest circle you can paint. Round to the nearest tenth of a foot goo qrr 7r b. Suppose you have-two cans 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. t/ V c. Does the radius of the circle double when the amount of paint doubles? Explain. no, to t d o tth 4-ke, pa #9 0,0 con) 40 toaft2 C creis) h tr it acifu4 otici ho! 11.3 a -6, /12 3. Suppose a squirrel is in a tree 24 ft above the ground. She drops an acorn. if' Nati "drop ah lied/ b a. Write a quadratic function for this situation. Then graph the function. h -1.6et O = -/ v-ft' s -L I, secs. = (= What is a renonable domain and range for the function? GrE 2 -V bt C- 1149)*, = iro4 ti) veloci-ty A 12 3 ^ -b (Se c) 4. Solve each equation by finding square roots. 1 a. 3d 2 _ = O cPN = 3 0 _3 b. 7h =1.24 7h2 =lja 7 a[2- de137-1

5 5. Find the value a. A rea a a -1-rleth le bk of h for each triangle. If necessary, round to the nearest tenth. b. da WO T1 hi PI VT) 2h JO (c2h)( 1-)) ii ao a h 3 6.-F Iliff= ILO t 6. The sides of a square are all increased y 3 cm. The area of the new square is 64 cm2. Find the length of a side of the original square. _X 1 Areit Qç sbaart 64 X +3)0(4-3) x 2 X- X+ 11)(X 7. 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? Area_ a ct, recfarui e go =610,, 3)1.0 2.Ki+15 0, go ;2W230 ;21, tAY-990 Gt 4-islau.4 I b9 6 -ph- 8. The product of two consecutive numbers is 14 less than Yu times the smaller number. Find each number. x smaller (x+-1) /0)( X+I bi/ge" _ x2" =it) X xl -qx4-14 (x 0 9. Solve x 2 = x and x 2 = x by factoring. What number is a solution to both equations? x X' = V' X z-- X-71 Az, 0,

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= 16/2 + 29t + 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 + 29t +6. W. % t2,L3.2-L-3i +4, b 3C-t- O RA--3)(t 7-a t t b. Graph the related function for the equation in art (a)'. Use your graph to estimate the maximum height of the ball. AOS X-.1-6Z-go s cioc25- MAX qt)6a5y4 aqc. 7(tA5)1 9 ) 19) 11. Suppose the area of the sail shown in the photo is 110 ft2. Find the dimensions of the sail. A Ito 2Uf-1 1,1 z X 2.4- X (d)(4-d,) "'= x 2-4-1( No + ID X =3 10 ovc+a 12. A square table has an area of 49 ft2. Find the dimensions of the table. h ME =111111WWIREMBIIIIII B MIIIIIIIIMINIII M MMIE 11111M M M ffill IIIMIMMFAMEN EMEIMIIIMIll MMEIMMINIII INIIIIIIIIIIIMI M MINIIIIIMMOIN MEMMENIIIIIIMIll 13. Solve the cubic equation: x3 10x2 + 24x = 0 X(X.0 / 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? r Areol BC' B. A 44('X+0 x 2 fr 4-16)(X-0 -ect Area a Skrian ct = x+-6

7 10.3 and 10.4 Part 5 : Word Problems Read each problem carefully and solve-by factoring or taking square roots., I. 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. 00( 6x ow h 6k )(-- 5,x a 2. 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. qo 3 VT 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 = J./ 014 dkh --- 0/ /01. _7 0 h -70 nl 4 7 h (0-1- 1z)(11

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9 Hour: Name: Solving Quadratics by Completing the Square (10.5 Part A) Solve by completing the square. 1. x2 4x =5 x 2_ X2-0 = (x a)a = ii&et c 2. x2 +10x = 21 2 odd bc1141 sides Fac-1-Dr r bah sides z X-=3 ) X -;2-3 4-a 1-:?. remember soiv e 2 eq. -s Solve by completing the square. 3. x2 +6x-91=0 co x 2 4-6x x 1 (lit 9 x 2 4-6X-1-4_11- ) X+3 *10

10 Solve each equation by completing the square. 5. x2-12x- 45 = 0 X x 2-2x = 48 X X 2-2X -0 q9 1177(-7i P/ X-1 ± 7 A_H --1 X-1 X x2-6x-16 = 0, 2. 7 c2,5 25 X-3' c)] 9. x2-14x -72 = 0 z 114A 4491 )( 2-1t-iX+ )21 IT O( 7Y X-7 = -I- tri:11 X =It ) )(-7 = x2-16x+28= 0 A2 16A X 1 112/r R)z 69- I - - -

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

12 Solve each equation by completing the square. 5. x2 7x = 0 6. x 2 +5x= 6 7. x2 4x= 8. x2 +4x-12 =0 9. x2 +11x+10=0 10. x2 +2x =15

13 Hour: 0.41 divide by a ic poicitle e -,916-1 smeaer Solve each equation by completing the square. Solving Quadratics by Completing the Square (10.5 Part C) 1. 2x2 +8x = x2 +12x = = X 1-4X -1-14Y1 :: 5 41)(4-q.? (7x.T: 2)a ff x-t- z 6 *.= /6 I 3. 5x2 +5 =10x. = 4. 4x2-12x = 40 /0 (351= A 2-3X q 4 X zJ6x = -30 X 4X -15 A d efp-- - X L-1X x -4) 2 lfl I am-li x x2 + 6x -9 = 0 3 2X-3 0 A2 4-2)< 3 ( x - 3 I.

14 Solve each equation by completing the square. 7. 2x2-16x+7 = x 2 X = 9 ±3 X -L- I_L-73) -= X X 10 base,- to 4-A lb + to 8. 3x2 +30x = A 2 4- ibx 141-1P 16 +,25 A z + 10X (X f 5)2 I X+5 I -7 2( n 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, find the value of x. Area of Rect./kJ-20e y A= base x X+/5 ±- 15,11 PX-i-JoYx 4,Q0) 15,21 #50 e/1( /r ADA IS -IS- c2/ " &OA S O.2 x 3bX ct gds" a5-0 I, a tizo x 2 4 _ 30/0. q ± ( -15go /5 10. 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. x(x+10)::-,1)( 4-10 A I ak-ftsi.dr2 /VX 078" /V 4 5% 5X4- (1)2 1 1/-4 (X 4-35-Y _11 gi V x 2 - ±1_ n

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 ) X 2 8x +5 = 0 ) x2 12x 91= x2 x =132 _II O rn 6. 14x2 =56 0? ) 9 (

16 Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth. 7. 5x2 =17x+12 x= 17± rag? 4,29-0.2(5-) X/7 ±23 /0 ID 8. 4x2-3x +6 = 0 X 3J r-g7 9. x2-6x = -9 x2.---6x x2 +6x-8=0-3± 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? I 1 2+1(14o4-2 to -xi (A/4-1q)(X-4-1/) 't4ct 12. 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 = -16t2 + vt + s to find out how long it will take for the ball to hit the ground. -05