Answer: y = 3x2 48 g(x) = f(x) 6 x = -1 and x = -7 g(-x) = af(-x) 4 = a(-3 + 2)(-3 1) f(x) = -x2 + 4x + 2 y = 2(x-2)2 The owners of a dog shelter want to enclose a rectangular play area on the side of their building. The graph of f(x) = x2 is narrower than the graph of g(x) = x2 when a > 0. Maximum value: 18, Question 19. In Exercises 6972, write the cubic function represented by the graph. The graph of f(x) = x2 is wider than the graph of g(x) = x2 when 0 < |a| < 1. As the function is increasing, the rate of change also increases. Use the other point (0, 6) to find the value of a: In the given function g(x) = \(\frac{1}{2}\)(x 1)2 + 1 we have f(-x) = -5x Answer: 51.4 = a(1.11)20 Answer: = -(-4)/2(-4) = -1/2 k(x) = x2 8x + 7 Answer: If x = 2 -3(2) + 4 = -2 Compare the graph to the graph of f(x) = x2. Answer: x = (p + q)/2 a. Since a>0, the minimum value for function exists. Answer: Does changing the sign of a change the x-intercepts? by . Answer: Write a quadratic function whose graph has a vertex of (3, 2) and passes through the point (4, 7). Given function, Finding y-coordinate for x = 29, we get that (29, 225) lies on the graph. g(x) = \(\frac{2}{3}\) x(x + 8) If x = 3 -3(3) + 4 = -5 y = 5x(x + 2)(x 6) Explain your reasoning. HOW DO YOU SEE IT? The given is a cubic function. The vertex is (-3, 2). y = 32. f(x) = -(x + 5))2 6 f(x) = -5x2 + 10x + 7 Explain. Since (2, -2) lie on the graph, The function is odd if it satisfies: System E: y = x2 x 30 0 = -2x2 + 6x + 8 Answer: Answer: Question 74. b. 0 = 4a + 8 Explain. g(x) = \(\frac{1}{2}\)x2 2- 6 = \(\frac{1}{2}\)x2 8, Question 12. Welcome to the Free Easy Access Student Resources portal for Big Ideas Math. 3x2 27 = 0 x = 0 or x = 1, Question 82. The y-intercept is 3. Answer: Question 5. a = -20 and b = 280 passes through (1, 0) and (7, 0) -2 = -4a At (1, 9): 9 = a + b Does the stronger rope have four times the diameter? Yes, starting at 13 days of vacation, the price for sea breeze is greater than blue water. Draw a picture of a word problem before writing a verbal model. -2x2 4x + 3 Tinyvilles population increased by 8% each year. Answer: The error is that the graph g(x) = x2 10 is the graph of f(x) = x2 translated down by 10 units instead of up. Answer: Question 44. = 3x2 + 2. f(x) = 128 . = 3(4) 2 2 Answer: Question 37. Vertex: (2, -4) n = 280/2(-20) = 7 a. a. Graph h. You add 48 square feet to the patio, resulting in a total area of 192 square feet. Step 4: Draw a parabola through vertex and x-intercept points. Identify characteristics of each parabola, if possible. r(x) = \(\frac{1}{4}\)(x + 10)2 Does changing the value of p change the x-intercepts? Which balloon reaches its maximum height faster? = 4 16 + 5 Which waterfall follows the narrowest path? The softball attains the maximum height at the vertex. a = -1/2 Which expressions are equivalent to (b-5)-4? a. Do you think students will like the game and want to play it? Three cars start traveling at the same time. Write a function that has constant second differences of 3. g(x) = (x + 1)2 7 The graph of h(x) is a horizontal translation right 5 units of the graph of f(x) What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax2? Plot the points (4, 0) and (-4, 0) Question 107. We observe that the two graphs have the same domain, range, axis of symmetry and are both parabolas. For each acorn, write an equation that represents the height h (in feet) as a function of the time t (in seconds). Therefore the vertex of the parabola is at (0, -4), Tell whether the table of values represents a linear, an exponential, or a quadratic function. Which aircraft hangar is wider? y0 = h(x0) Question 47. Answer: p(x) = \(\frac{1}{3}\)x2 2 x = -b/2a Justify your answers. Use graphs to justify your answer. y = (x + 3)(x 3) y = \(\frac{3}{4}\) x2 + 9x 18 b = 1/4 The main difference between the two graphs is that the graph of the given function is the graph of f(x) = x2 translated up by 1 unit. A professional basketball players shot is modeled by the function shown, where x and y are measured in feet. Let f(x) = 3x2 1 and g(x) = f (x) + 3. MODELING WITH MATHEMATICS Can a function be symmetric about the x-axis? f(x) = 2x2 + 12x + 5 Write the function f in standard form. (b) Predict which account will have a greater balance after 10 years. average rates of change from t = 2 to t = 7 y = \(\frac{1}{2}\)(x 1)2 + 3 The zeros also the x-intercepts: 3, 7 Thus the correct answer is option C. Question 7. ERROR ANALYSIS Graphing Quadratic Functions How are the graphs in Monitoring Progress Questions 1-8 similar? To explore the answers to this question and more, go to The point appears to represent a quadratic function with an axis of symmetry of x = -1. Question 42. Let g(x) = af(x) Answer: Question 39. How many grams of fat are in the burger that contains 600 calories? The U-shaped graph of a quadratic function is called a parabola. Throughout each chapter, students develop their mathematical skills by following the Explorers research and creating STEM connections. Vertex: (6, 0) The height of the football is represented by g(x) = f (x + 5). f(x) = a(x p)(x q)(x r) In Exercises 7174, describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. w(-x) = 5-x= \(\frac{1}{5x}\) Answer: The formula should be -b/2a x 1 = 0 or x 3 = 0 or x + 3 = 0 (120 6n) represents the unit price so we need to find the value of n where R is maximum which is located at the vertex. Answer: The graph is a translation right 6 units and a vertical shrink by a factor of 1/3 of the parent function. x = 9/4 = -4 + 8 Explain. Equation must have a vertex at (1, 2). Compare the graph to the graph of f(x) = x2. y = x2 9 Connect the highest point of one leg with the lowest point of the other leg. Answer: vertex: (5, -2); passes through (7, 0) Question 93. Answer: 0 = -x + 7 y = -(3)(-3) They are listed in the following fashion. a vertical stretch by a factor of \(\frac{1}{2}\) Question 1. ft. Use any 2 points, Answer: Question 34. Since the graph has a vertex of (-2, -3), the equation must be y = a(x + 2)2 3 Round your answer to the nearest tenth. Compare the graph to the graph of f(x) = x2. (2)0 y = 45x. COMPARING FUNCTIONS 3. g(x) = -3(x + 1)(x + 7) x = 2 -72 = a(1 +3)(1-4) He conducted meta-analyses and compared the . Determine whether the function is even, odd, or neither. x 4 = 0 or x + 2 = 0 To help determine the shape of the graph, find the points between the zeros and plot them. Question 25. f(x) = (x 2) + 1 The first differences are: 15, 25, 35 y = 2x2 10x + 13 Master the subject Maths and get different questions from the Practice Test, Chapter Test, Cumulative Practice. Answer: Using the graphing utility, the model is: Students engage through the online learning environment which includes real world connections, enrichment, and remediation when necessary while teachers have the ability to evaluate understanding by tracking student success rate, error analysis, and ability to express their understanding through mathematical writing.". x + 3 = 0 or x + 1 = 0 Answer: f(x) = -5(x + 7)(x 5) f(x) = \(\frac{1}{4}\)x2 6 After how many seconds does the pinecone hit the ground? Answer: Question 40. Math Algebra 1 Online Support Algebra 1 Online Resources Algebra 1 Online Resources Geometry . Write the function. Question 91. The range is (-, 12], Tell whether the function has a minimum value or a maximum value. Answer: y = 0 4 y = -2(2)2 + 8(2) + 24 Explain. a. Complete each function using the symbols + or , so that the graph of the quadratic function satisfies the given conditions. Using Zeros to Write Functions 9a = -19 You can solve Algebra 1 Big Ideas Math Textbook Questions easily by referring to our High School BIM Algebra Answers provided. 16y 4, Question 50. Draw the isosceles triangle shown. WRITING MODELING WITH MATHEMATICS t t1 = m(t t1) y = 3(1/3)2 2(1/3) Question 1. Use the point (0, 8) to find the value of a: Maximum value is 12. Where is the vertex of the cross section located? Question 29. For p(x): Big Ideas Learning Description The Assessment Book contains reproducible blackline master assessment materials for teachers to use throughout the year. Find the axis of symmetry of the graph of the equation y = ax2 + bx + c when b = 0. Answer: Question 4. g(-x) = f(-x) + ah(-x) Graph the axis of symmetry x = -9 + 3/2 = -3 f(x) = 2(x 1))2 + 1 Does the player make the shot? Describe two algebraic methods you can use to find the zeros of the function f(t) = -16t2 + 400. The axis of symmetry is given by x = (-1 + 4)/2 = 1.5, Question 26. where (4, 0) and (6, 0) are zeros Ace up your preparation and Develop Problem Solving Skills by referring to the Ch 8 Graphing Quadratic Functions Big Ideas Math Book Algebra 1 Solution Key. REASONING Plot the points (7, 0) and (3, 0) Given, Big Ideas Learning, LLC. Answer: Compare the graph to the graph of f(x) = x2. At(4, 0): 0 = 16a + 4b Answer: m(-x) = 2x2 + 7x ( 0, \(\frac{1}{4}\)), (1, 1), (2, 4), (3, 16), (-1, \(\frac{1}{16}\)) In Exercises 712, find (a) the axis of symmetry and (b) the vertex of the graph of the function. The x-coordinate of the vertex is -0.5. f(x) = a(x + 3)2 + 5 a reflection about the x-axis y = 2x2 + 8x + 3 -4x2 + 2x 6 (0, 8), (-4, 0.25), (-3, 0.4), (-2, 1), (-1, 3) Explain your reasoning. Answer: x = undefined because of division by 0. Compare the speeds of the three cars. f(x) = 5(x 3)2 1; g(x) = (x) 6 Let f, h be odd function. Describe the equation and graph of each type of function. Answer: x = 1 or x = 3 or x = -3. 425430), Graph the function. (0, -3), (1, 0), (2, 9), (-2, 9), (-1, 0) f(x) = (x + 4)(x + 1) x2 4x 13x + 52 = 0 (x + 1)2 = 0 f(x) = -(x + 1))2 2 x + 6 = 0 or x 6 = 0 or x 11 = 0 y = -(x 6)2 5 Answer: Answer: Answer: Question 30. Answer: Question 38. The x-intercepts are -3 and 4. At (2, 5): 0 = a(2) + b20) + c CalcChat and CalcView supplement classroom instruction by providing. Open Access Materials Answer: Question 5. x = -4 or x = -3 or x = 3 Question 27. x = 24/2(4) = -3 f(x) = -3x2 + 3x 4 y = -x 2x + 8. Answer: Given, Describe the domain and range of the function. x = \(\frac{b}{2a}\) Graph the function above and graph y = x2 f(4) = f(3) + f(2) = 2 + 1 = 3 Plot the corresponding points: (-9, 0), (-3, 0), (0, 0) Organization A begins with one donation, and the number of donations quadruples each hour. a. If a common ratio exists consecutive y-values, an exponential function must be used to model a data set. The graph is a line so the function is: Function D (-1, 2), (-2, 8), (-3, 32), (0, \(\frac{1}{2}\)), (1, \(\frac{1}{8}\)) Learners are able to bring problems from . a 2 unit shift to the left Differentiate Answer: Answer: The graph of the function passes through the point (0, -3). x = -(-6)/2 . y = -3x2 + 6x + 9 . Answer: Question 92. Work with a partner. = -4 8 + 1 We can see that in the consecutive y-values, each subsequent y-value is divided by 4. Woodrow Wilson high School. y = x2 2x + 7 Answer: Use the vertex form: MODELING WITH MATHEMATICS Using Your Book . Answer: b = 9 a 8.2 Graphing f(x) = ax2 + c (pp. (2)x Simply tap on the respective chapter and prepare whichever topic you feel difficult and allot time accordingly. The error was in solving the equation x2 9 = 0 in a wrong way. Use the intercept form: Explain your reasoning. b. This graph is a vertical shift of 3 units downward and a horizontal shift of 1 unit to the right. Use the drop-down menu below to select your program. The path of the tennis ball after you return a serve can be modeled by the function y = -0.005x2 + 0.17x + 3, where x is the horizontal distance (in feet) from where you hit the ball and y is the height (in feet) of the ball. Substitute c = 0 x2 2x + 1 + 6 Answer: f(x) = 1(x 4) + 8 y = -1/3 a = -3 Answer: The graph represents a linear function. x = -1. Answer: Question 20. The axis of symmetry is x = 2, so the x-coordinate of the vertex is 2. Describe why your answer makes sense considering the context of the data in Exercise 20 on page 466. Also, you can refer to the covering Questions from Practice Test, Chapter Test, Cumulative Practice, Performance Test, etc in this Chapter 8 Big Ideas Math Answer Key. (-2)2 + 8(-2) + 5 If x = 1 2(1) 3 = -1 = 4 B? Answer: Question 3. x = -1/3 WRITING Complete each table and sketch all three graphs in the same coordinate plane. Write a model for each pattern. y = 6 So, the vertex is (1, -9) f(x) = \(\frac{1}{2}\) x2 4x + 3 g(x) = -f(x). The domain is the set of real numbers. Plot the points (3, 0) and (-4, 0) The graph of a quadratic function is shown. How can you compare the growth rates of linear, exponential, and quadratic functions? If x = 3 3 + 5 = 8 f(x) = 6(x + 3)(x 4), Question 80. The range is [-9, +), Question 16. f(x) = -4(x + 3)2 + 1 = (0 8)/2 = -4. If x = 4 -3(4) + 4 = -8, Question 3. -27 = a(9)(9 10) q(x) = \(\frac{1}{2}\)x2 Answer: Now substitute 1888 for x in the equation to find the y-coordinate of the vertex. Given, Answer: Explain how you can use your height estimate to calculate a. c. How far does the arrow travel? Function is even if f(-x) = f(x) and function is odd if f(-x) = -f(x) Then determine the type of function that best represents this situation. Use the other point (-1, -36) to find the value of a Pumpkin reaches a maximum speed 2.75 seconds after it is launched and the maximum height is 133 feet. = -7, Question 9. Reflected in the x-axis Answer: Big Ideas Math Answers main intention is to provide good quality of education and make students move on the right path. THOUGHT PROVOKING The range is [-13, +), Question 15. f(x) = (x 2) + 1 Question 29. This will help you recall the information while taking a test. Then, learn thoroughly & solve all BIM Algebra 1 Ch 8 Graphing Quadratic Functions Questions covered in the chapter test, quiz pages. Point 1: (0, -2) y = -(x + 5)(x 1) Construct a table comparing the two resorts. Answer: Question 28. f(-x) = f(x) Answer: For simplicitys sake we will use (-1, 0), (1, 0) and (2, 0) f(x) = 2x2 + 1; g(x) = f(x) + 2 So, the vertex is (-2, -1) Answer: y = -4 y = 0.00016(1888)2 0.46(1888) + 507 = 203 y = abx We are given that (119, 0) lies on the graph. b. Given the x-intercepts (0, 10) use the intercept form We can see in graph that domain is set of all real numbers, R and range is (-, 16]. Therefore the point (12, 10) must also be on the graph. How to Solve Big Ideas Math Algebra 1 Textbook Questions easily? f(x) = ax2 + bx + c You and your friend both drop a ball at the same time. Question 43. x(x 1) = 0 y = -2x2 + 6x + 8 Answer: The highest point on the parabola is (0, -5). The axis of symmetry is x = 6 In Exercises 1316, describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. Given, Function is even if f(-x) = f(x) and function is odd if f(-x) = -f(x) Boswell, Laurie; Big Ideas Learning, LLC Boxid IA40320904 Camera USB PTP Class Camera Collection_set printdisabled External-identifier urn:oclc:record:1301804939 urn:lcp:bigideasmathalge0000lars_c4s3:lcpdf:43feba2e-89dc-4012-8ca3-5561757632b0 Answer: CRITICAL THINKING Answer: f(x) = a(x +3)(x-4) Question 25. Work with a partner. -16t12 + 16t1 = 0 Answer: MODELING WITH /MATHEMATICS g(x) = 2x Second Difference: 1, 1, 1 Since x = \(\frac{b}{2a}\) represents the x-coordinate of the vertex, the f(-\(\frac{b}{2a}\)) is the y-coodinate of the vertex. p(x) = \(\frac{1}{2}\)(x + 1)2 1 Vertically shifted 8 units upward In Exercises 7780, all the zeros of a function are given. How does the graph of y = ax2 + c compare to the graph of y = ax2? h(x) = -x2 f(12) = f(11) + f(10) = 89 + 55 = 144 System B: The x-intercepts are 5 and 3 Since f, h are even functions. d. The graph is a parabola so the function is Function A. we have a vertical stretch by a factor of \(\frac{3}{4}\) of the parent function y = x2, Question 4. Answer: Answer: Just tap on the chapter you need as a part of the preparation and get better grades in your exam. Write the function represented by each graph. Answer: Answer: Answer: Question 4. Answer: Question 86. range: y 10 Find another point on the parabola. f(x) = 3(x 3)2 + 6 Question 35. a. y = \(\frac{1}{2}\)x2 11x + 6 Question 17. Compare the graph to the graph of f(x) = x2. Answer: Therefore the data must represent an exponential function with a base of 0.5 or 1/2. 15 = a(4 6) + k Find the zeros of the function f(x) = kx2 k2x 2k3 in terms of k. See below for a quick preview of our new and innovative program, Algebra 1, Geometry, and Algebra 2 for grades 9-12. Given, y = 5(x 3) + 2, Graph the quadratic function. x(x 1) = 0 (a) Compare the account balances by calculating and interpreting the average rates of change from t = 2 to t = 7. MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) find the value of x that maximizes the area of the figure and (b) find the maximum area. p = and q = 7 To find 2 equations let a be any constant value other than 0 What do you notice about the x-coordinate of the vertex of each graph? b(x) = 2.5x2 2. Answer: h(x) = 2(x 4)2 Work with a partner. Describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. The trajectory of the pumpkin will be a parabola, so the time required for the pumpkin to reach maximum speed is actually the x-coordinate of the vertex of the parabola and the maximum height is the y-coordinate of the vertex. This corresponds to Graph B. a> 1 Answer: g(x) = 2x2 4x f(x) = -5(1)2 + 10(1) + 7 Answer: Question 14. MATHEMATICAL CONNECTIONS ANALYZING RATES OF CHANGE Answer: t0 = \(\frac{16}{2(-16)}\) Answer: Describe the transformation(s) from the graph of f(x) = |x| to the graph of the given function. Neither, Question 10. r(-x) = -6(-x)2 + 5 Answer: Question 20. = -4(-2)(2) = 16 g(x) = 5(x + 1)(x + 2) Step 1: The x-intercepts are 3 and -4. x + 1 = 0 or x 1 = 0 a. Thus the range is [0, 18] Compare the rate of change using average rate of change = f(b) f(a)/b-a Answer: ABSTRACT REASONING In Exercises 2629, determine whether the statement is always, sometimes, or never true. Answer: Answer: Question 22. Let g(x) = af(x) g(-x) = af(-x) The function y = a(x-h) + k has vertex as (h, k) and derived from the parent function y = x by various transformations: vertical shift of |k| units, horizontal of |h| units, vertical stretch or contraction (0 < |a| < 1) and reflection about the x-axis Question 5. Waterfall 2 h = -3.5d2 + 1.9 g(x) = 3x2 12x + 12 Given, Answer: What are some of the characteristics of the graph of f(x) = a(x p)(x q)? Answer: y = \(\frac{1}{2}\)x2 + 7x 4 h(x) = 8x2 8 g(x) = \(\frac{2}{3}\) x(x + 8) The initial height is the y-intercept which is y = 1.5 a = 1 Question 31. Answer: Plot the points. The domain of the function is all real numbers. For the given graph the x-intercepts are 6 and 10. y = a(x + 2x 8) Substitute in 0.5 for x and you get 4 for y Substitute the intercepts and simplify: Approximate the slope of the tangent line to the graph of y = x2 at the point (1, 1). passes through (-5, 0), (4, 0), and (3, -16) . f(x) = a(x h)2 + k It was treated as a linear equation, but it is a quadratic equation that can be solved either directly with the square root method or by factoring the expression and applying the zero product property. Answer: Question 48. VOCABULARY Question 43. Answer: Question 64. g(x) = 3x2 Given, h(x) = x(x2 1) The graph of g is a horizontal translation h units right if h is positive or |h| units left if h is negative and a vertical translation k units up if k is positive or |k| units down if k is negative of the graph of f. Question 4. Write and graph a quadratic function that models the path of the are with a maximum height of 300 meters, represented by a vertex of (59, 300), landing in the water at the point (119, 0). f(x) = -x2 + 49 Which account will have a greater balance after 10 years big ideas math algebra 1 26 practice a shrink by a factor of 1/3 of the must! Given, answer: therefore the data must represent an exponential function with a of... Your program Question 20 = 29, we get that ( 29, we get (. Than blue water word problem before writing a verbal model difficult and allot time.... Information while taking a test -3 ) They are listed in the consecutive y-values, an exponential must. Observe that the graph to the Free Easy Access Student Resources portal Big... Why your answer makes sense considering the context of the preparation and get better grades your... Sense considering the context of the graph is a translation right 6 units and a shift... 3 units downward and a horizontal shift of 3 units downward and a vertical by. A verbal model ( b ) Predict Which account will have a balance! Explain how you can use your height estimate to calculate a. c. far... Lowest point of the equation y = ax2 + c ( pp the Explorers research and creating connections... 27 = 0 or x = 1, 2 ) vertex at ( 1, 2 2... Lowest point of the preparation and get better grades in your exam find the zeros of vertex... And a horizontal shift of 1 unit to the graph of each type of function g ( )... Softball attains the maximum height at the vertex of the cross section located -1/2! A quadratic function is all real numbers, the price for sea breeze is greater than blue.... 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