Chapter 3. Resources by Chapter. Copyright Big Ideas Learning, LLC Algebra 2 All rights reserved.

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1 Chapter Famil and Communit Involvement (English) Famil and Communit Involvement (Spanish) Section Section Section Section Section Section Cumulative Review

2 Name Date Chapter Quadratic Equations and Comple Numbers Dear Famil, Have ou ever noticed that when a baseball is hit, the path of the ball is in the shape of a parabola? Quadratic equations can also be used to model the path of a baseball with respect to time. An eample of the path of a baseball is shown in the graph below. Height (feet) h Time (seconds) t The ball is hit feet from the ground, so the initial height h o is. From the graph, ou can also see that the ball is in the air for about. seconds and reaches a maimum height of about 80 feet. Working together, list five to ten sports that involve an object whose height with respect to time is in the shape of a parabola. For each sport: Determine a reasonable value for the initial position of the object. Determine a reasonable domain for the time the object is in the air. Determine a reasonable range for the height of the object. Graph the path of the object. Consider the following questions: What does the -intercept represent for each graph? What determines how long an object is in the air? What determines the height that the object travels? You can use the Internet to learn more about the applications of quadratic equations in sports. In this chapter, ou will find an equation to model the path of an object and learn several techniques for finding the -intercepts of the graph of a quadratic function. Net time ou are at a sporting event, notice how man different applications of parabolas ou see! 56 Algebra Copright Big Ideas Learning, LLC

3 Nombre Fecha Capítulo Ecuaciones cuadráticas números complejos Estimada familia: Alguna vez se han dado cuenta de que cuando se golpea una pelota de béisbol, la traectoria de la pelota tiene forma de parábola? Las ecuaciones cuadráticas también pueden usarse para representar la traectoria de una pelota de béisbol con respecto al tiempo. Un ejemplo de la traectoria de una pelota de béisbol se muestra en la siguiente gráfica. Altura (pies) h Tiempo (segundos) t Se golpea la pelota a pies del suelo, entonces la altura inicial ho es. Según la gráfica, también pueden ver que la pelota está en el aire durante casi. segundos alcanza una altura máima aproimada de 80 pies. Trabajen juntos para enumerar entre cinco a diez deportes donde haa un objeto cua altura con respecto al tiempo tenga forma de parábola. Para cada deporte: Determinen un valor razonable para la posición inicial del objeto. Determinen un dominio razonable para el tiempo que el objeto está en el aire. Determinen un rango razonable para la altura del objeto. Hagan una gráfica de la traectoria del objeto. Consideren las siguientes preguntas: Qué representa la intersección con el eje para cada gráfica? Qué determina cuánto tiempo un objeto está en el aire? Qué determina la altura que recorre un objeto? Pueden consultar en Internet para aprender más sobre los usos de las ecuaciones cuadráticas en los deportes. En este capítulo, hallarán una ecuación para representar la traectoria de un objeto aprenderán varias técnicas para hallar las intersecciones con el eje de la gráfica de una función cuadrática. La próima vez que vaan a un evento deportivo, fíjense cuántos usos diferentes de las parábolas ven! 57

4 . Start Thinking Graph equations =, =, =, and = in a coordinate plane. Label the equations. Make a chart to show the number of -intercepts of each equation, along with the corresponding point(s) of the -intercept(s). Are there an patterns ou notice? What are the? How can ou tell when the verte will be the minimum of the graph? The maimum?. Warm Up Use a graphing calculator to find the solution to the sstem of equations, if possible.. + = 5 =. = 6 = 5. + = = 6. + = 6 + =. + = = = 8 + = 5. Cumulative Review Warm Up Graph the function. Label the verte and ais of smmetr.. f( ) = ( + ). g ( ) ( ) = 6. 5( ) = +. f( ) = + 58 Algebra Copright Big Ideas Learning, LLC

5 Name Date. Practice A In Eercises 6, solve the equation b graphing = = 0. 5 = 0. = 0 5. = 6. = 5 In Eercises 7 9, solve the equation using square roots. 7. t = g = 6 9. ( + ) = 6 0. Describe and correct the error in solving the equation. ( ) + 6 = 5 + = ± 5 + = ± 5 = ± 5 = and = 7 In Eercises, solve the equation b factoring.. 0 = +. + = 6. m + m = 0 In Eercises and 5, find the value of.. Area of triangle = 7 5. Area of circle = 9π In Eercises 6 9, solve the equation using an method. Eplain our reasoning. 6. c 8 = 7. 7v = v p + = 9. 5 = 0 8. ( ) 0. Write a quadratic function in the form zeros and. f ( ) b c = + + that has 59

6 Name Date. Practice B In Eercises 6, solve the equation b graphing.. = 0. 6 = +. = = 5. = 6 6. = + 6 In Eercises 7 9, solve the equation using square roots. 7. ( k ) = 8. ( ) + = 5 9. = Write an equation of the form ( a) + b = d that has (a) two integer solutions, (b) two irrational solutions, and (c) no real solutions. In Eercises, solve the equation b factoring.. 0 =. k + k = k + k. w w 7 = w +. = 6 In Eercises 5 and 6, solve the equation using an method. Eplain our reasoning = 0 6. n.5 = In Eercises 7 0, find the zero(s) of the function h ( ) = g( ) = 0. j ( ) = 6 f ( ) = A local kaak rental shop rents 8 kaaks per week when it charges $5 per da. For each $5 increase in price, the shop loses four kaak rentals per week. How much should the kaak rental shop charge to maimize weekl revenue? What is the maimum weekl revenue?. You drop a coin into a fountain from a height of 5 feet. Write an equation that models the height h (in feet) of the coin above the fountain t seconds after it has been dropped. How long is the coin in the air? 60 Algebra Copright Big Ideas Learning, LLC

7 Name Date. Enrichment and Etension Solving Quadratic Equations In Eercises, use square roots or factoring to solve.. The hpotenuse of a right triangle is times one of the legs. The other leg is 5 units. Find the length of the hpotenuse.. One leg of a right triangle eceeds the other leg b inches. The hpotenuse is 0 inches. Find the length of the longer leg.. When a number is added to its square, the result is 6. What is the number?. The length of a rectangle is 8 units greater than its width. Find the dimensions when its area is 05 square units. 5. The difference of two numbers is and their product is. What are the numbers? 6. The product of two consecutive integers is 7. Find the integers. 7. The product of two consecutive even integers is 58. Find the value of each integer. 8. The sum of two numbers is 5 and the sum of their squares is 7. Find the numbers. 9. In 0 ears from now, m age will be the square of m age 0 ears ago. How old am I? 0. The dimensions of a rectangle were originall 0 units b units. The area of the rectangle increased b 5 square units, and the dimensions were increased b the same amount. Find the dimensions of the new rectangle.. A rectangular pool has a sidewalk around it. The pool measures 6 feet b 0 feet and the total area of the pool and sidewalk is 96 square feet. What is the width of the sidewalk?. A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool. The sidewalk is a constant feet wide. The total area of the pool and sidewalk is 60 square feet. Find the dimensions of the pool.. The area of a rectangle is 50 square inches. The length is 5 more than twice the width. Find the length of the rectangle.. The area of a triangle is 80 square centimeters. The base is less than twice the height. What is the height of the triangle? 6

8 Name Date. Puzzle Time How Can You Get Four Suits For A Dollar? Write the letter of each answer in the bo containing the eercise number. Solve the equation using square roots. Answers D. =. ( ) = 6. = 8 U. = 9; = 9. ( ) 8 =. ( ) 5 + = S. = 6; = Solve the equation b factoring = = 0 Y. = + ; = A. = ; = 7. 6 = 0 8. = C. = 8; = 8 Find the zero(s) of the function. 9. f( ) = f( ) = Solve the equation using an method.. 7 = 0. =.. ( ) = = = E. = 5; = K. = ; = B. = ; = F. = ; = C. = 0; = 7 A. = ; = 9 D. = 5; = 5 O. = ; = R. = + 6; = Algebra Copright Big Ideas Learning, LLC

9 . Start Thinking Enter the following kestrokes on a calculator. ENTER Describe what the calculator gives ou as a solution. Repeat the kestrokes with a different negative number. Wh does the calculator give this answer?. Warm Up Simplif.. ( ) + 6( + 6). 7( + 8) + ( + ). + ( + ). ( + ) ( 5 + ) 6. ( ) Cumulative Review Warm Up Identif the verte, focus, directri, and ais of smmetr of the parabola.. = ( + ). = ( + ) 7. = ( ). ( ) 8 5 = + 6

10 Name Date. Practice A In Eercises, find the square root of the number In Eercises 7, find the values of and that satisf the equation i = 5 + i i = + i 6. + i = + 8i i = 8 5i In Eercises 8, add or subtract. Write the answer in standard form. 8. ( + i) + ( 5 + 7i) 9. ( i) + ( 9 + i) 0. ( 6 + 5i) ( + i). ( 7 i) ( 0 i). Write each epression as a comple number in standard form. a b In Eercises 6, multipl. Write the answer in standard form.. 5i( + i). i( 8 i) 5. ( i)( + i) 6. ( + 6i)( 9 i) 7. Justif each step in performing the operation. ( i) + 5 i ( ) + 5 i i ( i) 9 i ( i i) i In Eercises 8 and 9, find the zeros of the function. 8. f ( ) = g ( ) = + In Eercises 0 and, solve the equation. Check our solution(s) = = 6 Algebra Copright Big Ideas Learning, LLC

11 Name Date. Practice B In Eercises, find the square root of the number In Eercises 7, find the values of and that satisf the equation.. i = + i 5. 6i = 8 i 6. + i = i = + i 5 In Eercises 8, add or subtract. Write the answer in standard form. 8. ( 9 + 6i) ( 5 7i) 9. ( i) i 0. ( 7 7i) + 8i. ( i) i. The additive inverse of a comple number z is a comple number za such that z + z a = 0. Find the additive inverse of each comple number. a. z = + i b. z = i c. z = 5 + i In Eercises 6, multipl. Write the answer in standard form.. ( + 7i)( 5 + i). ( 5 i)( 5 + i) 5. ( 0 7i)( 0 + 7i) 6. ( 6 i) 7. Justif each step in performing the operation. ( 6 i)( 8 i) 8 8i 6i + 6i 8 i + 6i ( ) 8 i + 6 i In Eercises 8 and 9, find the zeros of the function. g = 8. f ( ) = 8 9. ( ) In Eercises 0 and, solve the equation. Check our solution(s) = 8. = 5 65

12 Name Date. Enrichment and Etension Comple Numbers The comple conjugate of a comple number a + bi is a bi. For eample, the comple conjugate of i is +. i The sign onl differs on the imaginar part of the comple number. In Eercises 6, use the comple conjugate of the denominator to write the quotient in standard form.. + i. + i i. 5 + i 5 i. i i 5. + i i Comple numbers can be graphed in a coordinate plane called the comple plane. The horizontal ais is called the real ais and the vertical ais is called the imaginar ais. To graph a comple number such as + i, represent it, in the comple plane. Similarl, with coordinates ( ) the point (, ) represents. i + i 6. + i imaginar real In Eercises 7 8, graph the number and its comple conjugate in the comple plane i 8. i 9. 5i 0. i. + 5i. 6 i.. + i 5. 6i imaginar real 7. + i 8. + i 6 9. Describe the relationship between a comple number and its comple conjugate in the comple plane. 0. If the comple conjugate of a + bi is a bi, what can ou sa about the comple number a + bi? 66 Algebra Copright Big Ideas Learning, LLC

13 Name Date. Puzzle Time What Is The Difference Between A Pterodactl And A Parrot? A B C D E F G H I J K L M N Complete each eercise. Find the answer in the answer column. Write the word under the answer in the bo containing the eercise letter. 8i Find the square root of the number. i 5; i 5 THE A. 65 B. 90 SIT i 0 KNOW 5 i YOU D 6i 5 DIFFERENCE = ; = IF i ; i ON i EVER C. D. 8 0 Find the values of and that satisf the equation. E. + i = i + 9 F. 0 5i = + 5i Add, subtract, or multipl. Write the answer in standard form. G. ( 8 i) + ( + i) i H. ( + 7i) ( 8 i) I. i( + 7i) J. ( 6i)( + 6i) Find the zeros of the function. K. f( ) = 0 L. f( ) f = + 8 = + 75 M. f ( ) = + 8 N. ( ) 8 8i A i ; i YOUR 5; i 5i SHOULDER + i LET 5 PTERODACTYL = 7; = 60 YOU 67

14 . Start Thinking Simplif the epression ( + ). Eplain how to find the middle term and the last term of the resulting epression. Factor the epressions a + 6a + 9 and b + b + 9. If the constant term were missing from each polnomial, how could ou use the middle term to determine what the constant term should be?. Warm Up Factor the epression. 5z rs rs + r. Cumulative Review Warm Up Identif the function famil and describe the domain and range.. g ( ) =. g ( ) =. f ( ) = 6 +. h ( ) = + 5. f( ) = 0 6. f ( ) = 5 68 Algebra Copright Big Ideas Learning, LLC

15 Name Date. Practice A In Eercises, solve the equation using square roots. Check our solution(s)... + = 9. n 0n + 00 = = 9 p + p + 9 = In Eercises 5 8, find the value of c that makes the epression a perfect square trinomial. Then write the epression as the square of a binomial c c c c In Eercises 9, solve the equation b completing the square = 0 0. t t + 0 = 0. h 0h = 0 s + s 9 = 0. ( + 6) =. ( ) gg+ 0 = 6 In Eercises 5 8, determine whether ou would use factoring, square roots, or completing the square to solve the equation. Eplain our reasoning. Then solve the equation. 5. ( ) = = = = 0 In Eercises 9 and 0, find the value of. 9. Area of rectangle = 6 0. Area of parallelogram = In Eercises and, write the quadratic function in verte form. Then identif the verte.. f( ) = g ( ) = 6 69

16 Name Date. Practice B In Eercises, solve the equation using square roots. Check our solution(s)... w w + = 8. t 0t + 5 =. k 6k + 6 = 8 9p + 6p + = In Eercises 5 8, find the value of c that makes the epression a perfect square trinomial. Then write the epression as the square of a binomial c 6. + c c c In Eercises 9, solve the equation b completing the square. 9. qq+ ( 6) = 0. 5h 5h 5 = =. ( ) 8 = t t = + t. s + s = 6s + In Eercises 5 8, determine whether ou would use factoring, square roots, or completing the square to solve the equation. Eplain our reasoning. Then solve the equation. 5. ( + 9) = = 0 7. = = 0 In Eercises 9, write the quadratic function in verte form. Then identif the verte. 9. f( ) = g ( ) = 6. h ( ) = f( ) = +. The height (in feet) of a basketball t seconds after it is thrown can be modeled b the function = 6t + t +. a. Find the maimum height of the basketball. b. The basketball is caught in its descent when it is 7 feet above the ground. How long is the basketball in the air? 70 Algebra Copright Big Ideas Learning, LLC

17 Name Date. Enrichment and Etension Completing the Square In Eercises 6, complete the square to find the verte of each quadratic function. Continue to solve to find the -intercepts, if an. Use the information to graph and describe the transformation from the parent function f( ) =.. f ( ) =. f ( ) = +. ( ) f = f ( ) = f ( ) = ( ) f =

18 Name Date. Puzzle Time What Do You Call An Ice Skater Who Chats On The Internet? Write the letter of each answer in the bo containing the eercise number. Solve the equation using factoring, square roots, or completing the square.. ( + 8) = = 0 Answers K = ; = E. = ; = = 0. 5 = 0 N. 5 = ; = 5. = = 8 N. = + 6; = 6 L. = ; = = + 8. = I. =± 5 E. = ± 70 i = 0 0. = 8 8 S. = ; =. = = 5 A. = ± i 9 T. = ± 6 O. = ; = R. = ; = Algebra Copright Big Ideas Learning, LLC

19 . Start Thinking The four different was to solve a quadratic function covered thus far are listed below. Eplain when ou should use each one. Then use our opinion to arrange them in order from the wa ou are most comfortable using to least comfortable using. Completing the Square Factoring Graphing Using Square Roots. Warm Up Evaluate the epression when a =, b =, c = 0, and d =.. b c d. b d 5a. b d b +. ( ) 5. d b 9 b + a + bc + 6. b 0( ac bd) 5. Cumulative Review Warm Up Write a function g whose graph represents the indicated transformation of the graph of f. Use a graphing calculator to check our answer.. f( ) = 6 ; reflection in the -ais f = + 5; reflection in the -ais. ( ) 7

20 Name Date. Practice A In Eercises 8, solve the equation using the Quadratic Formula. Use a graphing calculator to check our solution(s) = =. + 5 = 6. 7 = = 0 = + = 6 = 9 In Eercises 9, find the discriminant of the quadratic equation and describe the number and tpe of solutions of the equation = 0 0. t t = = 0 + = 0. What are the comple solutions of the equation + 78 = 0? A i, 8 0i B i, 8 5i C. + 5 i, 5i D. + 0 i, 0i In Eercises and 5, find a possible pair of integer values for a and c so that the quadratic equation has the given solution(s). Then write the equation.. 5. a c = 0; one real solution a 5 + c = 0; two imaginar solutions In Eercises 6 and 7, use the Quadratic Formula to write a quadratic equation that has the given solutions ± 79 = 7. 8 = ± 97 6 In Eercises 8, solve the quadratic equation using the Quadratic Formula. Then solve the equation using another method. Which method do ou prefer? Eplain = = 0. + = 0 =. Suppose a quadratic equation has the form + + c = 0. Show that the constant c must be less than in order for the equation to have two real solutions. 7 Algebra Copright Big Ideas Learning, LLC

21 Name Date. Practice B In Eercises 8, solve the equation using the Quadratic Formula. Use a graphing calculator to check our solution(s) = = 0. + = 5 6. v = 0v = 0 5 = 0 6 = 5 = + t 8t 6 In Eercises 9, find the discriminant of the quadratic equation and describe the number and tpe of solutions of the equation = 0. h = h = + =. Determine the number and tpe of solutions to the equation 8 = 5. A. two real solutions B. one real solution C. two imaginar solutions D. one imaginar solution In Eercises and 5, find a possible pair of integer values for a and c so that the quadratic equation has the given solution(s). Then write the equation.. 5. a c + = 0; two real solutions a c = 0; two imaginar solutions In Eercises 6 and 7, use the Quadratic Formula to write a quadratic equation that has the given solutions ± 68 = 7. = ± 5i 8 In Eercises 8, solve the quadratic equation using the Quadratic Formula. Then solve the equation using another method. Which method do ou prefer? Eplain = 9. + =. + 0 = = 0. Suppose a quadratic equation has the form + + c = 0. Show that the constant c must be greater than in order for the equation to have two imaginar solutions. 75

22 Name Date. Enrichment and Etension Using the Quadratic Formula For Eercises 6, use the Quadratic Formula to solve for. B looking at the answer, could ou have factored?. ( + ) = ( ). ( + 5)( ) = ( 7)( 5 + ). ( ) = 6. ( ) = ( ) = = 6 8 For Eercises 7 9, determine the number and tpe of solutions the quadratic f 0 will have. Then graph f using the -intercepts, verte, and equation ( ) = other points. 7. f ( ) = 8. f( ) = + 9. ( ) = 5 f Make a statement about the relationship between the -intercepts of the graph of a quadratic function and the -coordinate of its verte. 76 Algebra Copright Big Ideas Learning, LLC

23 Name Date. Puzzle Time What Did The Couch Sa Halfwa Through The Marathon? Write the letter of each answer in the bo containing the eercise number. Solve the equation using the Quadratic Formula = 0 0 = = 0 Answers O. = ± i 6 A. = ± = 0 S. = ± = + = + = 6 0 = + = 7 = F. O. S. = ± 65 ± 5 = 5 5 ± 7 = 8 D. = 0; = O. = G. = ; = O. = ± i

24 .5 Start Thinking The solution to a sstem of linear equations is the point of intersection of the lines. If the lines are parallel, there is no intersection, so there is no solution. Given the following, sketch a possible graph of the sstem. Sstem with one linear equation and one quadratic equation, two points of intersection Sstem with two quadratic equations, one point of intersection Sstem with two quadratic equations, two points of intersection.5 Warm Up Solve the sstem using a graphing calculator.. = 9 =. = + =. = + 5 = 0. = = 6.5 Cumulative Review Warm Up Graph the function.. f( ) = ( 5). g ( ) ( ) = = 6( ) +. f( ) ( ) = 5 78 Algebra Copright Big Ideas Learning, LLC

25 Name Date.5 Practice A In Eercises, solve the sstem b graphing. Check our solution(s).. = + 6 = +. ( ) ( ) = + 6 =. = + = +. = = In Eercises 5 and 6, solve the sstem of nonlinear equations using the graph In Eercises 7 0, solve the sstem b substitution. 7. = = 8. + = 5 = = = 0. = 7 6 = In Eercises, solve the sstem using elimination.. 5 = + =. + = + 6 =. + 7 = + 8 =. = + 6 = A nonlinear sstem contains the equation of a constant function and the equation of a circle. The sstem has two solutions. Describe the relationship between the graphs. 79

26 Name Date.5 Practice B In Eercises, solve the sstem b graphing. Check our solution(s).. = + = +. = + 6 =. = ( + ) = 9. = ( ) = + In Eercises 5 and 6, solve the sstem of nonlinear equations using the graph In Eercises 7 0, solve the sstem b substitution. 7. = + = 9. + = 6 + = = 6 + = = = In Eercises, solve the sstem using elimination.. = 6 = 5. = 8 6 = + +. = + 8 = 8. 6 = + 50 = A nonlinear sstem contains the equation of a constant function and the equation of a circle. The sstem has one solution. Describe the relationship between the graphs. 80 Algebra Copright Big Ideas Learning, LLC

27 Name Date.5 Enrichment and Etension Solving Nonlinear Sstems Conic sections can all be written in the form A + B + C + D + E + F = 0 where A, B, and C are not all equal to zero. There are two cases: B = 0 (the aes of smmetr are parallel to the -ais or -ais) and B 0 (the conic sections are rotated). Tpe of conic Parabola: = ( h) + k AC = 0 Hperbola: ( h ) ( k ) a = AC < 0 b Coefficients Circle: + = r A = C, A 0, C 0 Eample: Classif the conic section defined b the equation 8 = + + and write it in standard form. Let B = = 0, where A and C. equation represents a hperbola. ( ) ( ) () ( ) ( ) ( + ) ( ) ( ) ( + ) = = Because AC < 0, the Because the equation is a hperbola, + 8 = isolate the constant = + Complete the square for and. + + = Simplif. + = Write in standard form. = Rearrange. In Eercises 6, let B = 0 and classif the conic section as a parabola, hperbola, or circle. Write the standard equation of the conic section.. 9 = 8 +. = + 6 = = = =

28 Name Date.5 Puzzle Time What Do You Get When You Cross A Rocket Ship With A Potato? Write the letter of each answer in the bo containing the eercise number. Solve the sstem b graphing, substitution, or elimination... = = = + = + 0. = + 5 = + + Answers U. ( 0.5, 5.5 ); (, 8 ) P. (.6, 7.5 ); (.6, 5.5) N. (, ); (, ) K. ( 8, 6 ); ( 6, 8) = + = + = 7 = + = + = + = 00 = S. (, ); (, ) D. ( 0, ); (, 0 ) I. no solution Algebra Copright Big Ideas Learning, LLC

29 .6 Start Thinking The following steps can be used to graph a linear inequalit. Replace the underlined words as needed to eplain how to graph a quadratic inequalit. Graph the line with = m + b. Make the line dashed for inequalities with < or > and solid for inequalities with or. Test a point (, ) above the line to determine whether the point is a solution to the inequalit. Shade the region above the line if the point is a solution. Shade the region below the line if the point is not a solution..6 Warm Up Graph the inequalit.. < 5. + > < 5.6 Cumulative Review Warm Up Solve the sstem of linear equations using the substitution method.. + 8z = 8 5 z = 57 7 z = z = 67 z = + z = 6 8

30 Name Date.6 Practice A In Eercises, graph the inequalit.. >.. 5. < In Eercises 5 and 6, use the graph to write an inequalit in terms of f( ) so point P is a solution P(, ) = f() = f() P(, ) In Eercises 7 and 8, graph the sstem of quadratic inequalities. 7. > 8. < < In Eercises 9, solve the inequalit algebraicall > < 9 In Eercises 6, solve the inequalit b graphing > > 7. An oceanfront lot has a perimeter of 50 feet and an area of at least 500 square feet. a. Write an inequalit describing this situation. b. Describe the possible widths of the oceanfront lot. 8 Algebra Copright Big Ideas Learning, LLC

31 Name Date.6 Practice B In Eercises, graph the inequalit.. +. > + < ( ) + 5. Describe and correct the error in graphing < +. < + In Eercises 6 and 7, graph the sstem of quadratic inequalities > + < + In Eercises 8, solve the inequalit algebraicall > < 9 In Eercises 5, solve the inequalit b graphing.. 6 > > 6. An object is dropped from a building. The height h (in feet) of the object after t seconds can be modeled b ht ( ) = 6t 8t + 5. a. At what height was the object initiall dropped? Eplain. b. Write an inequalit that ou can use to find the t-values for which the object was in the air. c. Based on our results from parts (a) and (b), use a graphing calculator to determine the time intervals in which the object was in the air. 85

32 Name Date.6 Enrichment and Etension Quadratic Inequalities You are a sales representative for a fashion and accessor wholesaler specializing in handbags. The price per handbag varies based on the number of handbags purchased in each order. Beginning with a price of $68 for one handbag, the price of each additional handbag purchased is reduced b $. Fill in the table to represent the prices and revenue of handbags. Number of handbags purchased 5 6 Price per handbag (dollars) Revenue per order (dollars) a. Write a function for the revenue. b. What is the maimum revenue per order? c. How man handbags must be purchased to attain maimum revenue? d. Assume that it costs $0 to produce each handbag and that ou spend an average of $ in fied costs per order. Based on onl these two factors, what is the function for the costs? e. In order to have a profit, the revenue must be greater than the costs. Write an inequalit for the profit. f. How man handbags do ou need to sell to make a profit? g. What is the maimum profit per order? How man handbags must be sold to earn the maimum profit per order? 86 Algebra Copright Big Ideas Learning, LLC

33 Name Date.6 Puzzle Time If Seagulls Fl Over The Sea, What Flies Over The Ba? Write the letter of each answer in the bo containing the eercise number. Match the inequalit with its graph. + <.. 5 Answers L. A G. F. 0 >. + 8 B. D A. C 5. < 6. + E. E S. B A. B. C D. E. F

34 Name Date Chapter Cumulative Review In Eercises, simplif In Eercises 5, find the sum or difference. 5. ( ) + ( ) 6. ( 7 + 0) ( 8 5) 7. ( ) + ( + 0) 8. ( 9) ( 9 + 6) 9. ( 8 ) ( 8 ) ( 6 ) ( 5 5 ). ( + 7) + ( ). ( ) ( ). ( ) + ( ). ( ) ( ) 5. After ou get on the school bus, there are si additional stops before ou reach school. The travel time between stops varies. The times (in minutes) between stops are.,.,.8,.7,.9,., and., respectivel. a. Each stop is 0.8 minute long. How long does it take to reach school from where ou get on the bus? b. Each stop is 0.9 minute long. How long does it take to reach school from where ou get on the bus? c. The total time ou are on the bus is. minutes. How long is each stop, if all the stops take an equal amount of time? 88 Algebra Copright Big Ideas Learning, LLC

35 Name Date Chapter Cumulative Review (continued) In Eercises 6 7, find the product. 6. ( 0 + ) 7. 5 ( ) 8. ( + )( + ) 9. ( )( ) 0. ( 5 + 0)( + 9). ( )( 7). ( + )( + 7). ( 5 )( ). ( 7 9)( ) 5. ( 8 + )( + 9) 6. ( + + )( + ) 7. ( + 9 6)( 6 + 0) In Eercises 8 59, simplif the epression. Write our answer in standard form. 8. ( ) 9. 5 ( + 5 0) 50. ( + )( + ) 5. 8( 9)( ) 5. ( )( + ) 5. ( + 7)( + ) 5. 6( )( 8 7) 55. ( ) 56. ( )( ) ( + + ) ( + 9)( ) ( )( ) During a school food drive, our class collects 7 nonperishable food items. a. How man total items are collected Tuesda through Frida if ou know there are items collected on Monda? b. Twent-nine items are collected on Wednesda, and the number of items collected on each of the remaining three das is the same. How man items are collected on Thursda? 6. You walk our dog each night. To walk the same route and distance, it takes our sister additional minutes and our brother fewer minutes. If it takes ou 9 minutes to walk our dog, how long does it take our brother and sister to walk the dog? 6. You are building a fence around a garden. The length is 5 feet more than the width. a. The perimeter is 66 feet. What are the length and width of the fence? b. Fence material is $6 per linear foot. How much will the fence material cost? c. Determine the area of the garden. 89

36 Name Date Chapter Cumulative Review (continued) In Eercises 6 77, solve the quadratic equation = = = = = = = = = = = = = = = 8 66 In Eercises 78 89, solve the equation for. 78. = = = = 8. = = = = = = 88. = = 5 In Eercises 90 0, evaluate b ac for the given values of a, b, and c. 90. a =, b =, c = 7 9. a =, b =, c = 9. a = 8, b = 8, c = 9. a = 7, b =, c = 8 9. a = 6, b = 9, c = 95. a = 7, b = 5, c = 96. a = 9, b =, c = 97. a =, b = 0, c = a =, b =, c = a = 6, b = 0, c = a = 6, b = 5, c = 0. a =, b = 6, c = 0 0. You and our friend are plaing basketball. Your friend makes more baskets than ou, and the total number of baskets ou both make is 8. a. Write an algebraic equation to represent the situation. b. How man baskets does our friend make? c. How man baskets do ou make? 0. You travel 65 miles for hours. a. What is our traveling rate? b. You travel at a rate of 5 miles per hour faster than the original rate. Now how long does it take ou to travel 65 miles? 90 Algebra Copright Big Ideas Learning, LLC

37 Name Date Chapter Cumulative Review (continued) In Eercises 0, solve the absolute value equation. Check for etraneous solutions. 0. = = = = = = = =. + = In Eercises, solve the sstem of linear equations.. =. + = 0 + = 5 = 5. + = 9 = = + = z = + z = z = z = 7 z = z = 7. + = 6 = z = z = + z =. + z = + z = 0 + z = 5 8. = + =. + z = + z = 7 z =. + z = 9 + 6z = z = In Eercises 5, add or subtract. Write the answer in standard form. 5. ( + i) + ( 6 + i) 6. ( + 5i) ( + 5i) 7. ( 7 + i) ( + 8i) 8. ( 9i) + ( 9i) 9. ( 6 7i) + ( + i) 0. ( 5 7i) ( 7 + i). 5 + ( 9 + i) ( i). ( 0 + i) + In Eercises, multipl. Write the answer in standard form.. i( + i) 5. 8 ( + 9i) 6. 6i( + 0i) 7. ( + 7i)( + 5i) 8. ( 8 + i)( 8 5i) 9. ( + 5i)( 7i) 0. ( 6 i). ( + i). ( 9 i). You bu dog food b the pound. It costs $0.85 per pound. a. How man pounds of dog food can ou purchase with $0? b. How much change will ou receive? c. There is a 7% sales ta on the dog food. How much is the new cost per pound? 9