Another birds dive is represented by r(t) = 2h(t). Answer: WRITING For this equation to be true, we can let a = c = 0 so that b can be any value. Answer: Question 62. The function y = -16x2 + 36 represents the height y (in feet) of an apple x seconds after falling from a tree. a reflection about the x-axis MODELING WITH MATHEMATICS Thus the initial velocity is 28ft/s. a. h(t) = -16t2 + 16t Question 5. Work with a partner. 12 = a(3 1)2 + 8 Answer: In Exercises 2126, tell whether the data represent a linear, an exponential, or a quadratic function. A water balloon is dropped from a height of 144 feet. y = \(\frac{1}{2}\)x2 + 7x 4 At what height does the firework explode? Answer: -27 = a(9)(9 10) b. f(x) = 2x2 + 12x + 4 Even. When making a review card for a word problem, include a picture. The function f(t) = -16t2 + 88t + 12 represents the height (in feet) of a pumpkin t seconds after it is launched from a catapult. we have a vertical stretch by a factor of \(\frac{1}{2}\) of the parent function y = x2, Question 3. ERROR ANALYSIS Big Ideas Math Answers Algebra 1 ensures your childs success and also keeps them on the right track. f(x) = 5(-1)2 + 10(-1) 3 Question 3. Answer: Waterfall 1 sends water the farthest. Note that there is a common ratio of 0.5 that you can multiply to get the next y-value. Which function could include the point (-2, 3)? f(x) = -5(x + 7)(x 5) Hence the vertex is (7, -14.5), Graph the function. Characteristics of Quadratic Functions, p. 420 3( x2 4x + 4) = 0 Parabola B can only be opening up and the vertex is at (3, -4) due to symmetry: Question 47. This is a set of 4 different versions of a test over Big Ideas Algebra 2 (Larson and Boswell) for Chapter 1. 8(x + 1)(x 1) = 0 Justify your answer. f(x) = \(\frac{1}{5}\)x2 5x + 27 As the graph passes through the point (4, 7). f(x) = a(x + 3)2 + 5 2 = a(0 + 2)2 + 6 Question 1. f(x) = -3(x + 3)(x + 1) -4 = m(1) 2 x = 1, 3, Find (a) the axis of symmetry and (b) the vertex of the graph of the function. Describe the domain of the function. Find the axis of symmetry and vertex: Big Ideas Math: A Common Core Curriculum (Red Edition) 1st Edition ISBN: 9781608404506 Alternate ISBNs Boswell, Larson Textbook solutions Verified Chapter 1: Integers Page 1: Try It Yourself Section 1.1: Integers and Absolute Value Section 1.2: Adding Integers Section 1.3: Subtracting Integers Section 1.4: Multiplying Integers Section 1.5: Describe the domain and range of the function. To find a, substitute either (-6, -4) or (6, -4) Answer: Question 4. a. The vertex is (-2, 0). Explain your reasoning. Answer: Question 30. How many grams of fat are in the burger that contains 600 calories? f(x) = a . You are standing 30 feet from the net, which is 3 feet high. State the vertex and axis of symmetry of the graph of y = ax2 + c. The axis of symmetry is 4a + 2b = 5 HOW DO YOU SEE IT? y = (x + 3)(x 3) 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. Plot the corresponding points: (-6, 0), (0, 0), (1, 0) Answer: (b) graph the function using any method. Comparing Speeds Let f(x) be an odd function. The function y = ax2 is derived from the parent function y = x2 by various transformation: vertical stretch (|a| > 1) or contraction (0 < |a| < 1) and reflection about the x-axis. x = \(\frac{-b}{2a}\) Answer: Question 1. f(x) = a(x 6)(x 10) Answer: Question 44. Vertex: (-4, 2) Direct link to Joscelyn Chilet's post How can I participate in , Posted 7 months ago. Answer: The axis of symmetry is x = -1. f(x) = (x 2) + 1 Big ideas math. Let k be a constant. If we write a graph in the form y = x2 2x + 7 After how many seconds does the pinecone hit the ground? y = 0.5x2 + \(\sqrt{2x}\) x 3 Find another point on the parabola. The scatter plot shows the amounts x (in grams) of fat and the numbers y of calories in 12 burgers at a fast-food restaurant. a. 0 = x2 + x 2 f(x) = -6x2 + 24x 20 h(x) = 3x2 2x What definition and characteristics of the graph of a quadratic function did you use to answer Exercise 44 on page 438? 1 g(x) = -2(x 4)(x + 1) How wide is the satellite dish? Answer: Hence the vertex is (-3, -4), Question 3. Thus the points (2, 0) and (-2, 0) lie on the graph. y = x2 x 12 Question 3. a. a vertical contraction by a factor of \(\frac{1}{2}\) Answer: Describe and correct the error in finding the axis of symmetry of the graph of y = 3x2 12x + 11. Which bird starts its dive from a greater height? g(x) = \(\frac{1}{4}\)x2 c. Describe where the function is increasing and decreasing. x = 6 or x = 1, Question 5. given, The domain of the function is all real numbers. d. Can the referee earn exactly $500? f(-3) = (-3)2 + 6(-3) 27 = -36 file Big Ideas Textbook Answers pdf. Question 41. -8x2 = -98 y = -(x 6)2 5 Use the vertex form: x2 4x 13x + 52 = 0 In Exercises 3742, use zeros to graph the function. f(x) = (x 4) + 8 = x 8x + 24. Are there more?? For r(x): g(x) = (x + 1)2 7 Answer: Question 18. The vertex is (-2, 4) Each graph represents a function of the form f(x) = (x p)(x q) or f(x) = -(x p)(x q). Answer: Using Your Book . = -4 8 + 1 (a) Compare the account balances by calculating and interpreting the average rates of change from t = 2 to t = 7. Substitute \(\frac{3}{4}\) for a and 9 for b In Exercises 2126, tell whether the function has a minimum value or a maximum value. a = -19/9 Explain. Answer: 5. x = 6, h = 6 Vertically shifted 8 units upward 5x2 9 Answer: Question 20. Answer: Answer: Question 74. vertical stretch by a factor of 3 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.". Answer: g(x) = \(\frac{2}{3}\) x(x + 8) Plot the points (-9, 0) and (3, 0) y = -14.5 y = 2(x-2)2 y = a(x + 4)(x 2) Answer: The function p(x) = \(\frac{1}{2}\)(x + 1)2 1 involves: p(x) = -5x2 10x 2 Do you support your friends claim? y = 1.5x 0.5x. The second differences are: -8, -8 (-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8) = 3x2 + 2. = -3/2(-3) = 1/2 = 0.5, Question 12. Direct link to Donna Brink's post Is there only 3 chapters , Posted 5 years ago. Answer: Given, f(x) = 3(x)(x 10) Step 2: h(t1) = 0 As a Big Ideas Math user, you have Easy Access to your Student Edition when you're away from the classroom. Question 19. Compare the graph to the graph of f(x) = x2. 3x2 12x + 12 = 0 Previous j(x) = 0.75x2 Axis of symmetry is x = 1 Question 3. Which balloon reaches its maximum height faster? Since the second differences are constant, then it is quadratic. Answer: Question 35. Any quadratic function can be written in standard form. g(x) = 2x2 + 1 + 2 Use the other point (0, 6) to find the value of a: f(x) = a(x p)(x q)(x r) Let a = 1 y = -3x2 + 6x + 9 Two intercepts are given (3, 0) and (13, 0) All Rights Reserved. Answer: When a quadratic function is in standard form, completing the square can be applied so that it can be transformed to vertex form. (-1, 2), (-2, 8), (-3, 32), (0, \(\frac{1}{2}\)), (1, \(\frac{1}{8}\)) How much should the store charge to maximize monthly revenue? g(x) = x2 + 6x + 5 = -24 + 48 20 f(x) = \(\frac{1}{2}\)x2 + 2x + 16 Compare the rate of change using the average rate of change a. ii. Answer: Question 28. y = 16(0) 4 m(x) = -2x2 + 6 We note that both graphs are parabolas and have the same range and axis of symmetry. Answer: f(x) = a(x h) + k f(-x) = 5(-x) h(x) = \(\frac{1}{4}\)x2 + 4 Answer: WHICH ONE DOESNT BELONG? Use a graphing calculator to verify your answers to Question 3. Answer: Question 22. Axis of symmetry is x = 0 Plot the points (0, 0) and (8, 0) f(x) = a(x)(x 10) \(\frac{4}{-12}\) = \(\frac{1}{-3}\), Question 44. f(x) = a . 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 We can see in graph that domain is set of all real numbers, R and range is (-, 32]. 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. If x = 3 \(\frac{1}{2}\)(3) 2 = \(\frac{7}{2}\) MODELING WITH MATHEMATICS where a = 3000, r = 0.2 Question 1. a. y = (x 3)2 How do you know that (-4, 2) is not the vertex? f(x) = mx 2 When does the pumpkin reach its maximum height? Question 4. y = (x + 5)(x + 3) Graphing y = ax2 + c The range is [-8, +). Answer: n(x) = \(\frac{1}{4}\)(x 6)2 Find values of a, b, and c so that the function f(x) = ax2 + bx + c is (a) even, (b) odd, and (c) neither even nor odd. y = 2(x+2)(x + 2) Question 10. THOUGHT PROVOKING Answer: Classify each system of equations by the number of solutions. Vertex: (-2, 0) Compare the graph to the graph of f(x) = x2. Graphing f(x) = ax2 + c, p. 426, Section 8.3 Pumpkin reaches a maximum speed 2.75 seconds after it is launched and the maximum height is 133 feet. ERROR ANALYSIS No, a only determines how narrow the function is and if it is reflected about the x-axis (if a < 0). 20 Answer: y = a(x h) + k 1 unit shift upward of the parent function y = x, Question 19. Write a quadratic function whose graph has a vertex of (1, 2). Answer: Find and interpret the x- and y-intercepts. R(n) = (120 6(5))(80 + 8(5)) = 10800 ERROR ANALYSIS Round your answer to the nearest tenth. a 4 unit shift to the left x2 17x + 52 = 0 f(x) = 3x 30x, Question 12. In his Visible Learning research, Professor John Hattie identified more than 250 influences on student learning and developed a way of ranking them. x = -(-6)/2 . Answer: MODELING WITH MATHEMATICS 4, 5, 9, 14, 23, . y = ax2 + c Answer: a = -6 Answer: Solve the equation. Question 18. Answer: Evaluate the expression when n = 3 and x = 2. range: y 5; passes through (0, 2) Answer: In Exercises 1518, tell whether the table of values represents a linear, an exponential, or a quadratic function. c. Compare the graphs. = 3, Question 10. passes through (-4, 0), (3, 0), and (2, -18) 3x 9 = 0 or 4x + 12 = 0 Question 10. The graph is a translation left 2 units and a vertical stretch by a factor of 2 of the graph y = x2. m = -4 + 2 Answer: If x = 2 -3(2) + 4 = -2 ERROR ANALYSIS Write a function that models the data. Question 5. f(x) = \(\frac{1}{4}\)(x 6)2 Question 36. Answer: What is the initial height of the arrow? f(x) = -5x2 + 10x + 7 x = 4 or x = 13, Question 26. 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