Name: Algebra 1 10.3 and 10.4 Part 3 Worksheet Hour: Solving Q adratics by Factoring and Taking Square Roots Worksheet 1. Match each grop.1 A.) its function. A. = x2 — I D. f(x) = 3x2 — 5 B. f(x) = x + 4 C. Px.) = —x2 2 CI E. f(x) = —3x2 + 8 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. h() What is the original height of the jumper? 0 ) What will the jumper's height be after 1 second? li- -160 ) 2.1,256 I) C What will the junk rsheight be after 3 seconds? u -3 ) h • How far will the jumper have fallen after 3 seconds? .75-6 -0 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. ----p h 110 NO) Tails 4,4 r ,sces 0.1 Name: Algebra 1 10.3 and 10.4 Part 4 Worksheet Hour: 10.3 and 10.4 Word Problems Worksheet 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-U4412 4-1LO - 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? = -/6•62' hvo: Mit "I 4 - Cse c) f. What values make sense for the domain? -tfiyi e 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 0 - I sec /6 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. iNo so g 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. 70-.2 qrr -goo 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/5.95... - V c. Does the radius of the circle double when the amount of paint doubles? Explain. no, 4-ke, pa 11-16- #9„0,0 con) 40 toaft2 C cReis) to t d o tth 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. GrE 2 -V bt if' Nati "drop° ah °lied/ b Write a quadratic function for this situation. Then graph the function. a. = -/ 6 1-16-6-2 0.14 A ^ = (= 12 v-FT' s -L I, 3 secs . -b (Se c) What is a renonable domain and range for the function? 4. Solve each equation by finding square roots. 1 = O a. 3d 2 _ 12 1- 3cPN = 0 _3 3 1149)* = iro4 ti) veloci-ty , h -1.6et O C- b. 7h2 +0.12 =1.24 7h2 =lJa 7 137-1 a[ 2- de a A rea a -1-rleth le bk 5. Find the value of h for each triangle. If necessary, round to the nearest tenth. a. b. (c2h)( 1-)) • JO da WO hi° PI ii T1— VT) ao a h 2h Iliff= ILO t 6.-F 3 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 sbaart Areit Qç 1 64 X +3)0(4-3) 64 x 2 “X- 64 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 go ;2W 230 2.Ki+15 0, ;21,0 2 1-3tAY-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 bi/ge" X+I 9. Solve x 2 = x and x 2 = (x+-1) /0)( _ x2 " =it) X xl -qx4-14 0 (x —x by factoring. What number is a solution to both equations? x X' = V' • X X-71 z-- Az, 0, 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. 0 17 ---16t2,L3.2-L -3i +4, b IIIMIMMFAMEN11111111111111111•1 11•1111111111111•11511111111111111111111111111111111 1111111110111111111111111EMEIMIIIMIll 3C-tO RA--3)(t 7-a h ME111111111=111111WWIREMBIIIIII 111111111B11111111111111MIIIIIIIIMINIII 11111111•1111111111111111M1111111111MMIE 11111M111111111.11111111M1111111111111111111111M 111111111•1111111111111.1111111111111111ffill t t 111111111111•111111111111111MMEIMMINIII INIIIIIIIIIIIMI11111121111111111111111.111M 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- s ci oc256Z-go 111111111111 11111111 111111 - -166 qt)6a5Y4 aqc. 7(tA5)1 1 1111111111111111111MINIIIIIMMOIN 111111111111111MEMMENIIIIIIMIll MAX 9 ) 19) 11. Suppose the area of the sail shown in the photo is 110 ft2. Find the dimensions of the sail. Ito ID X =3 10 + 2Uf-1 A (d)(4-d,) ovc+a 1 ,1°z X 2.4- X "'= x 2- 4-1( No 12. A square table has an area of 49 ft2. Find the dimensions of the table. 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? -ect — x+-6 A 44('X+0 Areol BC' B. x2 fr 4-16)(X-0 Area a Skrian ct = r 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: 2x 2 +6x = 20. Then determine if the graph of the related function would open up or down. 6x ow 00( 6k - h 0 4-3)(-- , 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 365 3. 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 = 0-11 80 J./ 014 dkh --- 0 / /01. 70 _ h - 70 nl 4 7 h (0 -1- 1z)(11 \L • Hour: Name: Solving Quadratics by Completing the Square (10.5 Part A) Solve by completing the square. ii&et 1. x2 —4x =5 x 2_ c odd X 2- 0 = (x—a)a = 2. x2 +10x = —21 2 bc1141 sides 24- 10 1- -Fac-1-Dr r bah sides remember z X-= 3 ) X -;2 -3 4-a 1-:?. soiv e 2 eq . -s- •--5 - Solve by completing the square. 3. x2 +6x-91=0 x 2 4-6x x°1 co (lit x2 4-6X-1- X+3 *10 9 4_11-__) Solve each equation by completing the square. 5. x2 -12x- 45 = 0 X - 0 7. x2 -2x = 48 8. x2 - 6x-16 = 0, 1177(-7i c2,5 q9 X 2- 2X -0 A_H---1 X-3'5 X-1 X -1-3 4-3 114A 10. x2 -16x+28= 0 4491 )( 2 -1t-iX+ A2 —16A )21 IT O( —7Y— tri:11 X-7 = -I=It ) )(-7 =-11 X 4-7 + ----- 4-3 413 --c )] -7- 9. x2 -14x -72 = 0 z 25 P/ 17-9-±7 X-1 I 7 2. X - X 1—112/r R)z 69- 6 Hour: /3 ° Name: Solving Quadratics by Completing the Square (10.5 Part B) . Solve by completing the square. 1. x2 —6x = 0 x2 4--b,k, + IL'x2 -3x=18 X — Solve by completing the square. 3. x2 +4x+4=0 -2 =0 Solve each equation by completing the square. 5. x2 —7x = 0 6. x2 +5x= —6 7. x2 —4x= 8. x2 +4x-12 =0 9. x2 +11x+10=0 10. x2 +2x =15 0.41 divide by a ic poicitlee- ,916-1 smeaer Hour: Solving Quadratics by Completing the Square (10.5 Part C) Solve each equation by completing the square. 1. 2x2 +8x =10 2. 2x2 +12x =32 • z 1- 0 =5 ---- *.= /6 6 X 1- 4X -1-14Y1 :: 5 41)(4-q. ? (7x.T: 2)a ff x-tI 3. 5x2 +5 =10x. 4. 4x2 -12x = 40 = /0 9 41- (351= A 2 - 3X -1 04 q 4 X5 am-LI 5 6. 3x2 + 6x -9 = 0 3 x 5. 2zJ6x = -30 2X-3 X 4X -15 A d efp-- A2 4- 2)< X L-1X -1-4 117 x -4) 2 lfl I x-- 3 I. 0 3 ( Solve each equation by completing the square. 7. 2x2 -16x+7 = -7 8. 3x2 +30x = -48 . 3 3 —7 —7 A 2 4- ibX 141-1P 16 +,25 A z + 10X lb x 2 —X I (X f 5)2 9 = q ±3 X+5 +5 ±3 -= X -L-I_L-73) n 2( -7 I 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-1-15 A= baSe x 10 PX-i-JoYx 4,Q0) e/1(‘2 4- 40/r ADA 4400 #50 X+/5 570 ±- 15,11 15,21 -IS -IS- 10 10 X X base,- to 4-A + to c2/ " &OA —S O 10 .2 3bX x x 2 4_ 30/0. I, a 12( -15go —/5 ct gdS" a5-0 tizo 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. ,1)( 4-10 A I ak-Ft si x(x+10)::- 2 - .DR2 /VX 078" 4- -55X4- (1)2 /V 4 11/-4 5% (X 4- 35-Y _11 gi V 4- x ±1_ n 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. g 1. X2 - 4x — 96 =0 3. X2 8x +5 = 0 — 5. x2 —x =132 2. x2 —36 = 0 ) 7 3 _II O rn 9( 6 ) -6 4. 4x2 —12x —91= 0 6. 14x2 =56 0? ) 6 .5 -3 Solve each equation by using the quadratic formula. If necessary, round to the nearest hundredth. 7. 5x2 =17x+12 8. 4x2 -3x +6 = 0 X 3J r-g7 x= 17± rag? 4,29-0 .2(5-) X/7 ±23 /0 ID 3 10 9. x2 -6x = -9 10. 2x2 +6x-8=0 x2.---6X+9 -3± 11. A rectangular painting has dimensions x and x + 10. 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 (A/4-1q)(X-4-1/) 't4ct 2+1(14o4-2 to 2 1 -- xi- 14 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
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