# Honors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations

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1 Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions) to solve problems. Use quadratic functions and inequalities to model and solve problems. a. Solve using graphs. b. Interpret the constants and coefficients in the contet of the problem. Da Date Lesson Assignment Tues. Feb. 5 Intro to Parabolas/Transformations Discover Education Activit(computer lab) Handout Packet p. Wed. Feb. 6 Summar of Transformations(notepacket p. ) Standard Form to Verte Form Verte Form to Standard Form, Applications Packet p. Thurs. Feb. 7 Quadratic Regression What do ou know about Factoring? Packet p. Fri. Feb. 8 Factoring: GCF, Grouping, Trinomials, Difference of Squares Packet p. 5 5 Monda March * Quiz on Sections Solving Quadratic Equations b Factoring Packet p. 6 6 Tues. March ACT Solving Quadratic Equations b Factoring and Graphing Packet p. 7 7 Wed. March 5 Review of Radicals Comple Numbers Brochure Project : Packet p. 8 EVEN 8 Thurs. March 6 Comple Numbers Solve b taking the square root Packet p. 9 #-7 odd, #-8 9 Fri. March 7 REVIEW Quiz on das 7-9 Work on Brochure Project Mon. March Complete the Square/Station Activit Packet p. Tues. March Discriminant Quadratic Formula Handout Wed. March Solving Quadratic Inequalities and Quadratic Sstems Packet p. &

2 Honors Algebra ~ Spring Name Thurs. March Review/Quadratic Applications Packet p. & 5 Fri. March Quadratic Functions TEST Packet p. 7 & 8 Finish Brochure Project Mon. March 7 BROCHURE PROJECT DUE!! Homework Grade: ******************************************************************* Homework Da Part : Identif the verte, the ais of smmetr, the maimum or minimum value, and the domain and range of each parabola. ) ) 5 ) Verte Verte Verte AOS: AOS: AOS: ma/min value ma/min value ma/min domain domain domain range range range Part : Describe how to transform the parent function to the graph of each function below. ) ( ) ) ( ) ) ( ) ) ( ) +5 5).5 + 6).( ) - Part

3 Honors Algebra ~ Spring Name Homework Da Write in Standard Form. Identif the verte and -intercept.. = ( ) +. = -( ) 6. = -( + ) 8. = ( 8) + 5. = -( + 7) 6. =.( 5.) + Determine whether the equations in each pair are equivalent. 7. = ( ) 7 8. = ( + ) + 8 = + = 6 + Match each equation with the correct statement. 9. = a. The verte is at (, ).. = ( ) + b. The -intercept is 5.. = ( 5) + c. The -intercept is.. = d. The verte is at (5, ).. The Galleria, in BCE Place in Toronto, has man beautiful parabolic arches. One of the arches can be modeled b the function = -.5( 6.8) + 6. The -ais represents the floor in the Galleria and the -ais represents the height above the floor. Distances are in meters. a. Write the function in standard form. b. What is the height of the arch at its center? c. The -intercept represents the lowest point at one side of the base of an arch. What is this height?. The height, h, of a baseball thrown off a bridge can be modeled b the equation h = -5(t ) + where the height is measured in meters and t is the time in seconds since the ball was thrown. a. How high was the ball thrown? b. How long did the ball take to reach its highest point?

4 Honors Algebra ~ Spring Name. A to rocket is shot upward from ground level. The table shows the height of the rocket at different times. Time(seconds) Height(feet) a. Find a quadratic model for this data. b. Use the model to estimate the height of the rocket after.5 seconds.. Suppose ou are tossing an apple up to a friend on a third-stor balcon. After t seconds, the height of the apple in feet is given b h 6t 8.t.96. Your friend catches the apple just as it reaches its highest point. How long does the apple take to reach our friend, and at what height above the ground does our friend catch it?. the barber s profit p each week depends on his charge c per haircut. It is modeled b the equation p c c 7. What price should he charge for the largest profit?. A skating ring manager finds that revenue R based on an hourl fee F for sakting is represented b the function R 8F F. What hourl fee will produce maimum revenues? 5. The path of a baseball after it has been hit is modeled b the function h. d d, where h is the height in feet of the baseball and d is the distance in feet the baseball is from home plate. What is the maimum height reached b the baseball? How far is the baseball from home plate when it reaches its maimum height? 6. A lighting fiture manufacturer has dail production costs of C.5n n 8, Where C is the total cost in dollars and n is the number of light fitures produced. How man fitures should be produced to ield a minimum cost? 7. Find a quadratic model for the data. Use 98 as ear. Price of First-Class Stamp Year Price(Cents) a. What is the quadratic model? b. Describe a reasonable domain and range for our model. (Hint: This is a real situation.) c. Predict when the cost of a stamp will be 5 cents. Is this valid? Wh or wh not?

5 Honors Algebra ~ Spring Name 5 Factoring Practice a a b + ab b k 8k z z c + c c k + k. a a + ad d. - 5 REVIEW: Part A: For each function, the verte of the function s graph is given. Find a and b.. a b 7; (, ). a b 5; (, ). a b 8; (, ). a b ; (,) Part B:. The equation for the motion of a projectile fired straight up at an initial velocit of 6 ft/s is h = 6t - 6t, where h is the height in feet and t is the time in seconds. Find the time the projectile needs to reach its highest point. How high it will go?

6 Honors Algebra ~ Spring Name 6 Factor each polnomial

7 Honors Algebra ~ Spring Name 7 Solving Quadratic Equations Solve each equation b factoring = =. n + 5 = n. 9z = z 5. 7 = 6. c = c w - 5w + 6 = 8. d + d + 5 = 9. 5v + 9v + 6 =. j + 6 = j. 6k = 5. m - 8m = 5m. 6e = 5e + 6e. 9 = 6p Solve each equation b graphing. Round each answer to two decimal places

8 Honors Algebra ~ Spring Name 8 Simplifing Epressions Containing Comple Numbers

9 Honors Algebra ~ Spring Name 9 Simplifing Epressions Containing Comple Numbers Continued Find the value of m and n for which equation is true. ) 8 5i m ni ) ( m n) ( m n) i 5 5i ) (m 5 n) ( m) i i ) ( n) ( m n) i 8 i Solving using square roots. 5) n 5 6) n 8 8 7) 8b 7 9 8) 85

10 Honors Algebra ~ Spring Name Completing the square: Homework da Solve each equation b completing the square. Give the eact answer.. a a. v 6v 65. p 6 p. n 8n r r 6. a a 8 7. m m k k 6. p p 6. m m. 7p 8p 5 Part : Find the value of k that would make the left side of each equation a perfect square trinomial.. k 5. k. k 6. 9 k 5. k 8 6. k

11 Honors Algebra ~ Spring Name Homework Da : Completing the square Solve each quadratic b completing the square. Give the eact answer Part : Solve b factoring, completing the square, or taking the square root ( )

12 Honors Algebra ~ Spring Name Quadratic Applications. A smoke jumper jumps from a plane that is 7 feet above the ground. The function = gives a jumper s height in feet after seconds. a. How long is the jumper in free fall if the parachute opens at ft? b. How long is the jumper in free fall if the parachute opens at 9 ft?. You want to epand the garden below b planting a border of flowers. The border will have the same width around the entire garden. The flowers ou bought will fill an area of 76 ft. How wide should the border be? ft 6 6. One side of a rectangular garden is d less than the other side. The area of the garden is 6 d. Find the dimensions of the garden.. An electronics compan has a new line of portable radios with CD plaers. Their research suggests that the dail sales s for the new product can be modeled b s = -p + p +, where p is the price of each unit. a. Find the verte of the function. b. What is the maimum dail sales total for the new product? c. What price should the compan charge to make this profit? 5. The shape of the Gatewa Arch in St. Louis is a catenar curve, which closel resembles a parabola. The function closel models the shape of the arch, where is the 5 height in feet and is the horizontal distance from the base of the left side of the arch in feet. a. Graph the function and find its verte. b. What is the maimum height of the arch? c. What is the width of the arch at the base?

13 Honors Algebra ~ Spring Name Graphing Quadratic Inequalities Solving Quadratic Inequalities Solve each inequalit. -- >. -+6 < z z 8. t < >

14 Honors Algebra ~ Spring Name. A ball is thrown straight up with an initial velocit of 56 feet per second. The height of the ball t seconds after it is thrown is given b the formula h(t) = 56t 6t. a. What is the height of the ball after second? b. What is its maimum height? c. After how man seconds will it return to the ground? d. When will the ball be 5 feet above the ground?. An object is thrown upward into the air with an initial velocit of 8 feet per second. The formula h(t) = 8t 6t gives its height above the ground after t seconds. a. What is the height after seconds? b. What is the maimum height reached? c. For how man seconds will the object be in the air?. A baseball is projected upward from the top of a 8 foot tall building with an initial velocit of 8 feet per second. The distance s of the baseball from the ground at an time t, in seconds, is given b the equation s = -6t + 8t + 8. a. Find the time it takes for the baseball to strike the ground. b. What is the baseball s maimum height?. A rocket is shot upward such that it s height in feet, h, is given as h = 6t 5t, where t is the number of seconds since liftoff. a. Approimate the length of time the rocket is above feet. b. When will the rocket hit the ground? Use the formula h( t ) vt 6t where h(t) is the height of an object in feet, v is the object's initial velocit in feet per second, and t is the time in seconds. 5. An arrow is shot upward with a velocit of 6 feet per second. Ignoring the height of the archer, how long after the arrow is released does it hit the ground? 6. A tennis ball is hit upward with a velocit of 8 feet per second. Ignoring the height of the tennis plaer, how long does it take for the ball to fall to the ground?

15 Honors Algebra ~ Spring Name 5 Review Sheet: Unit. The following function represents the height, h, of a rocket t seconds after it is launched: h = - (t.5) +. When does the rocket reach its maimum height?. Bob wants to fence in his backard using his house as one side of the fence. He has 5 ft of fencing available. Find the dimensions of the fence needed to maimize the area.. The function h = -6t + 5t + represents the height of a ball t seconds after it is thrown. Could it hit a kite fling feet in the air?. A ball is thrown up in the air with an initial velocit of 56 feet per second. The height of the ball t seconds after it is thrown is given b the formula h(t) = 56t 6t. What is the maimum height of the ball? When does it return to the ground? 5. Solve 7 - > 6. Solve Solve using an method: + = 8. Solve using an method = 9. State the discriminant and nature of roots: - 7. State the discriminant and nature of roots: -. Solve: 8. Simplif: ( 5 i) ( i) (5 6 i ). Simplif: i 9 i. Simplif: 5. Simplif: ( 5 i)( 6 i ) 6. Simplif: ( i ) 7. Simplif: 7 i i 8. A rectangular garden contains ft and has a walk of uniform width surrounding it. If the entire area, including the walk, is ft ft., how wide is the sidewalk? Factor Completel: 9) a a a ) ) m m 6 ) m m 7 ) 6 Find the verte and ais of smmetr: ) 7 5) 7 6) ( ) 7) Write the equation of a parabola that has a verte at the origin and passes through the point (, -6). 8) Write the equation of a parabola that has a verte at (, -7), and passes through (,-9). 9) Describe how the parabola ( ) is shifted/different from.

16 Honors Algebra ~ Spring Name 6 Answers to Review Sheet. Ma at.5 sec.. dimensions: 87.5 ft 75 ft. no (graphs do not intersect). Ma height: 9 ft., and returns to the ground after.5 seconds 5. 5 or and 8. 5 i 9. discriminant = -8, so imaginar roots. discriminant =, so real rational root. i. 6-i i. 8. i i 6. 6i 7. 7 i 8. foot 9. ( a )( a ). 8( )( ). (m+)(m-). (m-)(m+7). ( )( )( ). V=(, ); a of s: = 5. V=(.75, -6.5); a of s: = V=(,); a of s: = ( ) 7 9. more narrow, left, up

17 Honors Algebra ~ Spring Name 7 Cumulative Review Units -. The attendance at a ball game was people. Student tickets cost \$ and adult tickets cost \$. \$,5 was collected in ticket sales. Which sstem models the situation if s is the number of students and a is the number of a is the number of adults? A. s = a B. s = a C. s + a = D. s + a = (s + a) =,5,5(s + a) = s + a =,5 s + a =,5. What sstem describes this graph below? (tick marks are one unit apart) A. B. C. D.. Which of the following is FALSE? A. C. is the identit matri. B. D.. What is the solution of X has no inverse. is the identit matri for addition. 5? 6 A. 5 B. 5 C. 5 D. 5 E Which product does not eist? A. B. C. D Solve the formula for h. A ( b b ) h 7. A factor can produce products, and, with a profit of P = The Production of can eceed b no more than units. Also, production is limited b the Constraint. What production levels ield maimum profit? A. =, = B. =, = C. =, = D. =, = 6 8. What is the value of 7? A. B. 9 C. -9 D. -

18 Honors Algebra ~ Spring Name 8 a 6 6 b a 9. What are the values of a,b, and c if? 7 c 7 c A. a = -, b = 8, c = B. a = -, b =, c = C. a =, b = 8, c = - D. a = -, b =, c = -. What does z equal in the solution of the sstem z 8 z 7? z. What is the solution of in the sstem 6 5?. Write the equation of a line with slope 5 and passes through (, 9) in slope-intercept form.. For a campaign, a compan gave awa 5, tos to children. Tos and cost the compan \$.9 and \$.98, respectivel. The compan spent \$5,6. How man of to did the give awa? A. 9 B., C., D.,. Two pickup trucks have capacities of ¼ and ½ ton. The made a total of 8 round trips to haul 7 ½ tons of crushed rock to a job site. Which matri equation could be used to determine how man round trips each truck made? A B. 5. The Coast Guard flies a rescue out of Elizabeth Cit to Hatteras in the middle of a Nor easter. It takes them one hour with a headwind to fl one hundred miles to get there and thirt minutes to fl back. How fast was the wind and how fast was the plane in still air? 6. What is the equation of the graph of an absolute function that opens down with verte (,) and passes Through the point (6,)? A. B. C. D. 7. Solve. A. B. C. or D. or 8. What is i ( i) ( i) written as a comple number in standard form? C D A. 6i B. 6i C. i D. i 9. Which quadratic function has a verte of (-,) and passes through the point (,9)? A. B. C. D Solve A. 6 B. 6 C. D.

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