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Lesson 3.1 Extra Practice STUDENT BOOK PAGES 140–147 1. State whether the parabola opens up or down. a) f (x) ⫽ 4x 2 b) f (x) ⫽ ⫺3 (x ⫺ 6 ) (x ⫺ 8 ) c) f (x) ⫽ ⫺(x ⫹ 7 ) 2 ⫺ 9 d) f (x) ⫽ 9x 2 ⫹ 4x ⫺ 1 2. Given f (x) ⫽ ⫺2 (x ⫺ 7 )(x ⫹ 5 ) , state a) the zeros b) the direction of opening c) the equation of the axis of symmetry Copyright © 2008 by Thomson Nelson 3. Given f (x) ⫽ (x ⫺ 3 )( x ⫺ 4 ) , state a) the zeros b) the direction of opening c) the equation of the axis of symmetry 4. Graph each function. a) f (x ) ⫽ 2x 2 ⫺ 4 b) f (x) ⫽ (x ⫹ 1 ) 2 ⫺ 2 c) f (x) ⫽ 2 (x ⫹ 1 )(x ⫺ 2 ) 1 d) f (x) ⫽ ⫺ x 2 ⫹ 3 2 5. Express each quadratic function in standard form. State the y-intercept of each. a) f (x) ⫽ ⫺(x ⫺ 6 )(x ⫹ 5 ) b) f (x) ⫽ ⫺4 (x ⫺ 2 ) 2 c) f (x) ⫽ 5 (x ⫹ 3 ) 2 ⫹ 2 d) f (x) ⫽ 7 (x ⫺ 1 )(x ⫺ 8 ) y 6. 5 4 3 2 1 –4 –3 –2 –1 0 –1 –2 –3 x 1 2 3 4 For the parabola above: a) State the direction of opening. b) Name the coordinates of the vertex. c) List the values of the x-intercepts. d) State the domain and range of the function. e) Determine the algebraic model for this quadratic function. y 7. 6 5 4 3 2 1 –4 –3 –2 –1 0 –1 –2 x 1 2 3 4 Examine the parabola above. a) State the direction of opening. b) Find the coordinates of the vertex. c) What is the equation of the axis of symmetry? d) State the domain and range of the function. 8. Each pair of points (x, y) are the same distance from the vertex of their parabola. Determine the equation of the axis of symmetry of each parabola. a) (5, 5), (⫺5, 5) b) (4, 2), (⫺6, 2) c) (1, ⫺9) , (8, ⫺9) 1 1 d) a⫺2, b , a3, b 4 4 9. The height of a balloon above the ground is modelled by the quadratic function h(t) ⫽ ⫺2t 2 ⫹ 18t, where h(t) is the height in meters, t minutes after the balloon is launched. a) Graph the quadratic function. b) How long will the balloon be in the air? How do you know? c) How high will the balloon be after 3 minutes? d) What is the maximum height that the balloon will reach? Lesson 3.1 Extra Practice 405