Skills Practice Skills Practice for Lesson 1.1

Transcription

1 Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s 6 t 0t, where s is the height after t seconds. The acceleration from gravit is 3 feet per second squared, the initial velocit is 0 feet per second, and the initial height is feet. Problem Set Write an equation to represent the area of each rectangle.. A rectangle with a length that is 3 inches longer than its width A w(w 3) w 3w. A rectangle with a length that is inches shorter than its width A w(w ) w w 3. A rectangle with a width that is 8 feet shorter than its length A ( 8) 8. A rectangle with a width that is.6 feet longer than its length A (.6).6 Chapter l Skills Practice 5

2 Use the given information to answer the questions. 5. A neighborhood is made up of a series of square lots. Due to an increase in bike traffic, a bike lane is being added along the edge of the roadwa. The bike lane will decrease one side of each lot b feet. The equation A w(w ) represents the new area of each lot, where w is the width of the original lot. a. What is the new area of a lot that had an original width of 00 feet? A 00(00 ) 00(88) 37,600 square feet b. What is the new area of a lot that had an original width of 30 feet? A 30(30 ) 30(308) 98,560 square feet 6. A series of picture frames are made so that each has a length that is inches greater than its width. The equation A w w represents the area of each frame, where w is the width of the frame. a. What is the area of a frame with a width of 8 inches? A 8 (8) square inches b. What is the area of a frame with a width of inches? A () 68 square inches Complete each table Chapter l Skills Practice

3 Name Date Create a scatter plot of each data set Chapter l Skills Practice 53

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5 Name Date Use the given information to answer the questions. 5. A soccer ball is kicked upward with an initial velocit of 8 feet per second. The acceleration due to gravit is 3 feet per second squared. The equation s 6 t 8t represents the height of the ball, s, after t seconds. What is the height of the ball after a. second? s 6 () 8() s 6 8 s 3 The ball will be 3 feet in the air after second. b. 3 seconds? s 6 (3) 8(3) s 6(9) s s 0 The ball will be 0 feet in the air, or on the ground, after 3 seconds. 6. An arrow is shot upward with an initial velocit of 0 meters per second. The acceleration due to gravit is approimatel 0 meters per second squared. The equation s 0t 5 t represents the height of the arrow, s, after t seconds. What is the height of the arrow after a. seconds? s 0() 5 () s 80 5() s 80 0 s 60 The arrow will be 60 feet in the air after seconds. b. 5 seconds? s 0(5) 5 (5) s 00 5(5) s 00 5 s 75 The arrow will be 75 feet in the air after 5 seconds. Chapter l Skills Practice 55

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7 Skills Practice Skills Practice for Lesson. Name Date Parabolas Properties of the Graphs of Quadratic Functions Vocabular Identif and label each term in the diagram. ais of smmetr 0. parabola. verte 3. ais of smmetr. zeros parabola zeros verte 0 Problem Set Complete the table for each quadratic function Chapter l Skills Practice 57

8 Use each table to construct a graph of the given function Chapter l Skills Practice

9 Name 7. Date Use the given graph to determine the verte, ais of smmetr, and zeros of the parabola. 9. Ais of smmetr: Zeros: (0, 0) and (, 0) Verte: (, 3) Chapter l Skills Practice 59

10 0. Ais of smmetr: Zeros: (, 0) and (0, 0) Verte: (, 3) Ais of smmetr: Zeros: (, 0) and (0, 0) Verte: (, ) Ais of smmetr: 0 Zeros: (, 0) and (, 0) Verte: (0, ) Chapter l Skills Practice

11 Name Date Use the information provided to determine the ais of smmetr, -intercept(s), and -intercept of the parabola. 3. The verte of the parabola is (, 3) and it passes through the point (0, 0). Ais of smmetr: -intercept(s): (0, 0) and (, 0) -intercept: (0, 0). The verte of the parabola is (, 0) and it passes through the point (0, 6). Ais of smmetr: -intercept(s): (, 0) -intercept: (0, 6) 5. The verte of the parabola is (3, 0) and it passes through the point (0, 8). Ais of smmetr: 3 -intercept(s): (3, 0) -intercept: (0, 8) 6. The verte of the parabola is (, ) and it passes through the point (0, 0). Ais of smmetr: -intercept(s): (0, 0) and (8, 0) -intercept: (0, 0) Chapter l Skills Practice 6

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13 Skills Practice Skills Practice for Lesson.3 Name Date Etremes Increase, Decrease, and Rates of Change Vocabular Write the term that best completes each statement.. The rate of change of the unit rate of change is called the second difference.. A minimum or maimum point on a graph, such as the verte of a parabola, is called a(n) etreme point. 3. A(n) interval is the set of numbers between two given numbers.. A(n) open interval (a, b) is the set of all numbers between a and b, but not including a or b. 5. A(n) closed interval [a, b] is the set of all numbers between a and b, including a and b. 6. The notation [a, b) is used for the half-closed interval that is the set of all numbers between a and b that includes a, but does not include b. Problem Set Complete the table for each of the given quadratic functions Chapter l Skills Practice 63

14 Complete the table for each function b finding the change in and and the unit rate of change (slope) between each pair of points m m Chapter l Skills Practice

15 Name Date 7. m m Complete the table for each function b finding the unit rate of change ( ) and the second difference ( ). 9. ( ) Chapter l Skills Practice 65

16 0. ( ) ( ) ( ) Chapter l Skills Practice

17 Name Date Use interval notation to represent each set of numbers. 3. The set of all real numbers between 6 and 6, including 6 and 6 [ 6, 6]. The set of all real numbers between and 0, not including or 0 (, 0) 5. The set of all real numbers between 9 and 0, including 9 but not including 0 [ 9, 0) 6. The set of all real numbers between 5 and, including but not including 5 ( 5, ] 7. The set of all real numbers greater than (, ) 8. The set of all real numbers less than or equal to 6 (, 6] Determine the intervals over which each quadratic function is increasing or decreasing The function is increasing over the interval (, ) and decreasing over the interval (, ) The function is decreasing over the interval (, 3) and increasing over the interval (3, ) Chapter l Skills Practice 67

18 The function is decreasing over the interval (, ) and increasing over the interval (, + ). The function is increasing over the interval (, ) and decreasing over the interval (, + ). 68 Chapter l Skills Practice

19 Skills Practice Skills Practice for Lesson. Name Date Solving Quadratic Equations Reviewing Roots and Zeros Vocabular Describe how to find the roots of a quadratic equation b using the given method.. factoring If a quadratic equation is factorable, first set the equation equal to zero. Then factor the equation and set each factor equal to zero. Solve each resulting equation. The solutions to the resulting equations are the roots, or zeros, of the quadratic equation.. etracting the square roots If a quadratic equation does not have an -term (or if the -terms cancel out), solve the equation for a perfect square. Then, etract the square roots to determine the roots, or zeros, of the quadratic equation. Problem Set Calculate the roots of each quadratic equation b factoring. Check our answers ( 5)( ) or 0 5 or ( 5 ) 7( 5) ( ) 7( ) Chapter l Skills Practice 69

20 ( 3)( ) or 0 3 or (3 ) (3) ( ) ( ) ( 7)( ) or 0 7 or (7) 3(7) 9 8 ( ) 3( ) ( )( 3) 0 0 or 3 0 or 3 ( ) ; 33 8( ) (3 ) 9; 33 8(3) Chapter l Skills Practice

21 Name Date ( )( ) 0 0 or 0 or ( ) 7 ( ) 7 ( ) 7( ) (3 )( ) or 0 3 or 3 3 ; 3 ( 3 ) 3 ( 9 ) 3 3; 3( ) ( 5)( 5) or or 5 ( 5 ) ( 5 ( 5 ) ( 5 ) 5 ) 5 Chapter l Skills Practice 7

22 (3 )( 3) or or ( 3 ) ; 6 ( 6 3 ( 3 ) ) 6 ( 7 ; 6 ( 3 ) 6 ( 9 9 ) 8 3 ) 7 Find the roots of each quadratic equation b etracting the square roots. Check our answers (5 ) 5(5) 5 5( 5 ) 5(5) (9 ) 3 3(8) 3 0 3( 9 ) 3 3(8) Chapter l Skills Practice

23 Name Date. ( ) (7 ) 7(9) 63 9 (7) 9 63; 7( 7 ) 7( 5) 35 9 ( 7) ( ) (3 ) 9 3( ) 9 (3) ; 3( 3 ) 9 3( 7) 9 ( 3) ( 5 ) ( 5 ) ( 5 ) ( 5 ) Chapter l Skills Practice 73

24 ( 7 ) ( 7 ) 7 7 ( 7 ) ( 7 ) ( ) 6( ) ( ) 3 () 3() 6( ) 6() ; 3 ( ) 3 (0) 0 6( ) 6(0) 0 6. ( ) ( ) () () 0 () 0 8 ; ( ) ( 3) (9) 8 0 ( ) Chapter l Skills Practice

25 Skills Practice Skills Practice for Lesson.5 Name Date Finding the Middle Determining the Verte of a Quadratic Function Vocabular Describe how to determine the coordinates of the verte for each parabola.. a c, where a and c are real numbers and a is not equal to zero For all quadratic functions in this form, the ais of smmetr is on the -ais ( 0), so the -value of the verte is 0. The -value is c. The coordinates of the verte are (0, c).. a b c, where a, b, and c are real numbers and a and b are not equal to zero To find the verte of a quadratic equation in the form a b c, with b 0, first find the -intercept b evaluating the function at 0. Find the coordinates of the point smmetric to the -intercept b substituting the -coordinate of the -intercept into the equation. Use the midpoint formula on the two points to find the equation for the ais of smmetr. The -coordinate of the verte lies on the ais of smmetr. Calculate the -coordinate b evaluating the function at this -coordinate. Problem Set Determine the ais of smmetr and the verte for each quadratic function Ais of smmetr: 0 Verte: (0, 3). 9 9 Ais of smmetr: 0 Verte: (0, 9) 3. 7 Ais of smmetr: 0 Verte: (0, 7). 5 8 Ais of smmetr: 0 Verte: (0, 8) 5. ( ) Ais of smmetr: 0 Verte: (0, ) 6. ( ) Ais of smmetr: 0 Verte: (0, ) 7. Ais of smmetr: 0 Verte: (0, ) 8. 3 Ais of smmetr: 0 Verte: (0, ) 9. 6( 3) Ais of smmetr: 0 Verte: (0, 8) 0. ( ) Ais of smmetr: 0 Verte: (0, ) Chapter l Skills Practice 75

26 Determine whether the verte for each quadratic function is a maimum or minimum.. 3 minimum. 8 3 maimum 3. 7 maimum. minimum 5. ( 7 6) minimum 6. 5( ) maimum 7. (3 ) maimum 8. 3( ) minimum Determine the -intercept of the graph of each quadratic function (0 ) 3(0) 0 0 -intercept: (0, ) (0 ) 3(0) intercept: (0, 3). 6 (0) (0) intercept: (0, 6). 3 3 (0 ) 3(0) intercept: (0, 3) 76 Chapter l Skills Practice

27 Name Date (0 ) (0) intercept: (0, 8). ( ) ((0 ) (0) ) () -intercept: (0, ) Calculate the ais of smmetr for each set of smmetric points on a parabola. 5. (, 3) and (6, 3) 6 (, 3 3 ) (9, 3) Ais of smmetr: 9 6. (, ) and (6, ) ( 6, ( ) ) (5, ) Ais of smmetr: 5 7. ( 3, 8) and ( 9, 8) ( 3 ( 9) 8, ( 8) ) ( 6, 8) Ais of smmetr: 6 8. (, 5) and (, 5) (, 5 5 ) ( 5, 5) Ais of smmetr: 5 Chapter l Skills Practice 77

28 Find the coordinates of the point that is smmetric to the given -intercept for each quadratic function. 9. ( ), -intercept: (0, ) ( ) 0 0 ( ) 0 or 0 0 or ( 0 0 ) () ( ( ) ) () Point smmetric to -intercept: (, ) , -intercept: (0, 85) ( 8) 0 or or 8 (0) 8(0) ( 8) 8( 8) Point smmetric to -intercept: ( 8, 85) 78 Chapter l Skills Practice

29 Name Date 3. 3, -intercept: (0, 3) ( ) 0 or 0 0 or (0 ) (0) ( ) () Point smmetric to -intercept: (, 3) 3. (3 ), -intercept: (0, 8) 8 (3 ) 3 0 (3 ) 0 or or 3 0 or 3 (3(0 ) (0) ) (0 0 ) ( ) 8 ( 3 ( 3 ) ( 3 ) ) ( 3 ( 9 ) ( 3 ) ) ( 3 Point smmetric to -intercept: ( 3, 8 ) 3 ) ( ) 8 Chapter l Skills Practice 79

30 Use the -intercept and a smmetric point to find the coordinates for the verte of each quadratic function intercept: (0, 0) ( ) 0 or 0 0 or 0 (0) ( ) () Smmetric point: (, 0) -coordinate of verte: 0 6 -coordinate of verte: (6) (6) Verte: (6, 6) intercept: (0, 5) ( 0) 0 or or 0 (0 ) 0(0) ( 0 ) 0( 0) Smmetric point: ( 0, 5) 0 ( 0) -coordinate of verte: 5 -coordinate of verte: ( 5) 0( 5) Verte: ( 5, 0) 80 Chapter l Skills Practice

31 Name Date intercept: (0, 5) ( ) 0 or 0 0 or (0) (0) ( ) ( ) Smmetric point: (, 5) 0 ( ) -coordinate of verte: -coordinate of verte: ( ) ( ) Verte: (, 6) intercept: (0, 3) ( 0) 0 or or 0 (0) 0(0) (0) 0(0) Smmetric point: (0, 3) -coordinate of verte: coordinate of verte: (5) 0(5) Verte: (5, ) Chapter l Skills Practice 8

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33 Skills Practice Skills Practice for Lesson.6 Name Date Other Forms of Quadratic Functions Verte Form of a Quadratic Function Vocabular Answer each question about the given function.. What form is the quadratic function a b c written in? What do the variables a, b, and c tell ou about the graph of the function? The quadratic function a b c is in standard form. The variable a tells what direction the parabola opens. For a 0, the parabola opens up. For a 0, the parabola opens down. If the variable b 0, the verte of the parabola is on the -ais. The variable c is the -coordinate of the -intercept.. What form is the quadratic function a ( h) k written in? What do the variables a, h, and k tell ou about the graph of the function? The quadratic function a ( h) k is written in verte form. The variable a tells what direction the parabola opens. For a 0, the parabola opens up. For a 0, the parabola opens down. The variable h is the -coordinate of the verte. The variable k is the -coordinate of the verte. Problem Set Use the standard form of each quadratic function to determine the ais of smmetr, the coordinates of the verte, and whether the parabola opens up or down.. f( ) Ais of smmetr: b a ( ) f( ) () () 8 Verte: (, ) a 0, so the parabola opens up. Chapter l Skills Practice 83

34 . f( ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) Verte: (, 0) a 0, so the parabola opens up. 3. f( ) 6 Ais of smmetr: b a ( ) 6 f( ) (6) (6) 6 (36) Verte: (6, 56) a 0, so the parabola opens up.. f( ) 3 8 Ais of smmetr: b a ( 8 6 ) ( 3) 3 f( ) 3 (3) 8(3) 3(9) Verte: (3, 6) a 0, so the parabola opens down. 5. f( ) Ais of smmetr: 0 Verte: (0, ) a 0, so the parabola opens down. 6. f( ) 9 Ais of smmetr: 0 Verte: (0, 9) a 0, so the parabola opens up. 8 Chapter l Skills Practice

35 Name Date Use the verte form of each quadratic function to find the ais of smmetr, the coordinates of the verte, and whether the parabola opens up or down. 7. f( ) ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. 8. f( ) 3 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. 9. f( ) 6 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens down. 0. f( ) ( 3) 7 Ais of smmetr: 3 Verte: (3, 7) a 0, so the parabola opens down.. f( ) ( 3) Ais of smmetr: 3 Verte: (3, ) a 0, so the parabola opens up.. f( ) ( ) 3 Ais of smmetr: Verte: (, 3) a 0, so the parabola opens down. Chapter l Skills Practice 85

36 3. f( ) 8 ( ) 3 Ais of smmetr: Verte: (, 3) a 0, so the parabola opens down.. f( ) 5 ( ) Ais of smmetr: Verte: (, ) a 0, so the parabola opens up. Convert each quadratic function from verte form to standard form. 5. f( ) 6 ( ) f( ) 6( ) f( ) 6 f( ) f( ) ( 3) 7 f( ) ( 6 9) 7 f( ) 36 7 f( ) 9 7. f( ) ( 3) f( ) ( 6 9) f( ) f( ) ( ) 3 f( ) ( ) 3 f( ) 3 f( ) 86 Chapter l Skills Practice

37 Name Date 9. f( ) ( ) 3 f( ) ( 8 96) 3 f( ) f( ) f( ) 5 ( ) 0 f( ) 5( 8 6) 0 f( ) f( ) Convert each quadratic function from standard form to verte form.. f( ) Ais of smmetr: b a ( ) f( ) () () 8 Verte: (, ) Verte form: f( ) ( ). f( ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) Verte: (, 0) Verte form: f( ) ( ) 0 3. f( ) 7 0 Ais of smmetr: b a ( ) f( ) 7 () () Verte: (, 3) Verte form: f( ) 7 ( ) 3 Chapter l Skills Practice 87

38 . f( ) 8 Ais of smmetr: b a ( ) 3 f( ) ( 3) ( 3) 8 (9) Verte: ( 3, 6) Verte form: f( ) ( 3) 6 5. f( ) Ais of smmetr: b a 8 ) f( ) ( ) ( ) ( Verte: (, ) Verte form: f( ) ( ) 6. f( ) 6 Ais of smmetr: b a 6 3 ) f( ) ( 3 ) 6 ( 3 ) ( 9 Verte: ( 3, 5 ) Verte form: f( ) ( 3 ) Chapter l Skills Practice

39 Skills Practice Skills Practice for Lesson.7 Name Date Graphing Quadratic Functions Basic Functions and Transformations Vocabular Match each term with the graph that represents it.. translation. dilation 3. reflection. basic quadratic function Graph D Graph B Graph C Graph A A 0 8 B C D Chapter l Skills Practice 89

40 Problem Set For each quadratic function, describe (without graphing) how the equation and the graph have been transformed from the basic function.. The graph of the basic function was dilated b a factor of.. The graph of the basic function was dilated b a factor of The graph of the basic function was shifted up 5 units.. 8 The graph of the basic function was shifted down 8 units. 5. ( 3) The graph of the basic function was shifted right 3 units. 6. ( 6) The graph of the basic function was shifted left 6 units. 7. ( ) The graph of the basic function was reflected about the ais. 8. ( ) 3 The graph of the basic function was shifted up 3 units and shifted right units. 90 Chapter l Skills Practice

41 Name Date Determine the verte of each function. Use the verte and our knowledge of the shape determined b the value of a to graph the function. Then describe the graphical transformations that were used to transform the basic quadratic function to each given function. 9. ( 3) 0 Verte: (3, ) The graph of the basic function is shifted down unit and right 3 units ( ) 5 Verte: (, 5) The graph of the basic function is shifted up 5 units and left unit Chapter l Skills Practice 9

42 . ( ) 0 Verte: (, 0) The graph of the basic function is shifted right units and reflected over the -ais Verte: (0, 3) The graph of the basic function is shifted up 3 units and reflected over the -ais Verte: (, 6) Ais of smmetr: b a ( ) f( ) () () 8 6 The graph of the basic function is shifted down 6 units and right units Chapter l Skills Practice

43 Name Date. 8 0 Verte: (, ) 8 Ais of smmetr: b a 8 f( ) ( ) 8( ) 6 3 The graph of the basic function is shifted down units and left units ( ) 0 Verte: (, 0) 8 The graph of the basic function is shifted left units and dilated b a factor of Verte: (0, 3) The graph of the basic function is shifted up 3 units and dilated b a factor of Chapter l Skills Practice 93

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