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Chapter 10 Story Problems Domain x values Range y values Chapter 10 Story Problems Domain x values Range y values p. 633 #40 Find domain and range y = 0.012x2 Domain -32< x < 32 Range 0 < y < 12.288 Chapter 10 Story Problems Falling Objects - Two acorns drop from an oak tree. One falls 45 feet while the other falls 32 feet. Write an equation. h = -16t2 + vt + s h = -16t2 + 46 h = -16t2 + 32 Graph the equations and compare. The vertex is (0,46) and the other is (0, 32). Chapter 10 Story Problems Falling Objects - A pinecone falls about 25 feet from the branch of the tree. How long does it take to land on the ground? Write an equation. h = -16t2 + vt + s h = -16t2 + 25 0 = -(4t – 5)(4t +5) t = 1.25 sec. Graph the equation. Where does it cross the x-axis? Chapter 10 Story Problems Suspension Bridges - p. 637 #4 The cables between the Towers form a parbola with the equation y= 0.00014x2 -0.4x + 507 What is the height above the water at the -lowest point? X = -b/2a X = -(-0.4)/2(0.00014) = 1428.6 Y = 0.00014(1428.6)2 – 0.4(1428.6) + 507 = 221 ft. Graph the equation. Where does it cross the x-axis? Chapter 10 Story Problems Architecture - p. 639 #41 The parabolic arches that support The Convention Center can be modeled by the equation Y = -0.0019x2 + 0.71x What is the highest point? Graph the equation. What are looking for? Vertex? X-intercept? . Use the 2nd Calc key to solve. About 66 feet Chapter 10 Story Problems Architecture - p. 639 #41 The parbolic arches that support The Convention Center can be modeled by the equation Y = -0.0019x2 + 0.71x What is the highest point? Graph the equation. What are looking for? Vertex? X-intercept? . Use the 2nd Calc key to solve. About 66 feet Chapter 10.1/2 Review y = x2 + 4x + 4 y = -2x2 + 6 . Axis of symmetry X = -2 Vertex (-2, 0) Min or Max Min Opens Up or Down Up Axis of symmetry X = 0 Vertex (0, 6) Max Min or Max Opens Up or Down Down Graph the equation. Use the 2nd Calc key to solve. Chapter 10 Minimum or Maximum? y = 5x2 + 3x + 12 Minimum Graph upward y = -3x2 - 7x + 15 Maximum Graph downward y = x2 - 5x + 6 Minimum Graph upward y = -8x2 + 10x - 20 Maximum Graph downward . y = 4x2 - 5x - 25 Minimum Graph upward Chapter 10.1/2 Review y = -4x2 - 3 No Solutions y = x2 + 6x + 9 -3 y = x2 – 9x + 14 7, 2 Axis of symmetry X = 0 (0, -3) Vertex Min or Max Max Opens Up or Down Down Axis of symmetry X = -3 Vertex (-3, 0) Min Min or Max Opens Up or Down Up Axis of symmetry X = 4.5 Vertex ( 4.5, -6.25) Min or Max Min Opens Up or Down Up Chapter 10 Story Problems Sports Event – During an ice hockey game, a blimp flies 45 ft. above the crowd and drops a numbered ball. The number on the ball corresponds to a prize. Find the amount of time in the air. Graph the equation. What are looking for? Vertex? X-intercept? . h = -16t2 + vt + s About 1.7 sec Chapter 10 Solve the equation using the quadratic formula. 1) x2 + 4x + 1 = 0 -3.73 -0.27 2) X2 – 6x + 12 = 0 No solutions 3) X2 – 6x + 9 = 0 3 . Chapter 10 Solve the equation. 1) 2x2 – 20 = 78 7, -7 2) 3x2 – 7x + 2 = 0 .33, 2 3) 5x2 – 4x = 2 -.35, 1.15 . Chapter 10 Linear, Quadratic, or Exponential Function? X -1 0 1 2 Y 3 0 3 12 X 0 1 2 3 Y -5 -2 1 4 X 1 2 3 4 Y 1 2 4 8 Quadratic Linear . Exponential Chapter 10.1/2 Review y = 3x2 + 4 No Solutions y = x2 + 2x + 1 -1 y = -x2 – 7x + 8 -8, 1 Axis of symmetry X = 0 (0, 4) Vertex Min or Max Min Opens Up or Down Up Axis of symmetry X = -1 Vertex (-1, 0) Min Min or Max Opens Up or Down Up Axis of symmetry X = -3.5 Vertex ( -3.5,44.75 ) Min or Max Max Opens Up or Down Down Chapter 10 Solve the equation. 1) 2x2 – 20 = 0 3.16, -3.16 2) x2 – 2x = 15 -3, 5 3) 5x2 – 7x = -1 .16, 1.24 . Chapter 10 Linear, Quadratic, or Exponential Function? X -1 0 1 2 Y 1 0 1 4 X 0 1 2 3 Y 3 6 9 12 X 1 2 3 4 Y 1 2 4 8 Quadratic Linear . Exponential