Chapter 10 Story Problems

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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

y = x2 + 4x + 4 Graph the equation. Use the 2nd Calc key to solve. Chapter 10.1/2 Review Axis of symmetry Vertex Min or Max Opens Up or Down X = -2 y = x2 + 4x + 4 (-2, 0) Min Up Axis of symmetry Vertex Min or Max Opens Up or Down X = 0 y = -2x2 + 6 (0, 6) Max 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

y = -4x2 - 3 y = x2 + 6x + 9 -3 Axis of symmetry Vertex Min or Max Chapter 10.1/2 Review Axis of symmetry Vertex Min or Max Opens Up or Down X = 0 y = -4x2 - 3 (0, -3) Max No Solutions Down Axis of symmetry Vertex Min or Max Opens Up or Down X = -3 y = x2 + 6x + 9 (-3, 0) Min -3 Up Axis of symmetry Vertex Min or Max Opens Up or Down X = 4.5 y = x2 – 9x + 14 ( 4.5, -6.25) Min 7, 2 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

x2 + 4x + 1 = 0 X2 – 6x + 12 = 0 X2 – 6x + 9 = 0 3 No solutions . Chapter 10 Solve the equation using the quadratic formula. x2 + 4x + 1 = 0 X2 – 6x + 12 = 0 X2 – 6x + 9 = 0 -3.73 -0.27 No solutions . 3

Chapter 10 Solve the equation. 2x2 – 20 = 78 3x2 – 7x + 2 = 0 5x2 – 4x = 2 7, -7 .33, 2 . -.35, 1.15

. Chapter 10 Linear, Quadratic, or Exponential Function? Linear X 1 2 -1 1 2 Y 3 12 Quadratic X 1 2 3 Y -5 -2 4 Linear . X 1 2 3 4 Y 8 Exponential

y = 3x2 + 4 y = x2 + 2x + 1 -1 Axis of symmetry Vertex Min or Max Chapter 10.1/2 Review Axis of symmetry Vertex Min or Max Opens Up or Down X = 0 y = 3x2 + 4 (0, 4) Min No Solutions Up Axis of symmetry Vertex Min or Max Opens Up or Down X = -1 y = x2 + 2x + 1 (-1, 0) Min -1 Up Axis of symmetry Vertex Min or Max Opens Up or Down X = -3.5 y = -x2 – 7x + 8 ( -3.5,44.75 ) Max -8, 1 Down

2x2 – 20 = 0 x2 – 2x = 15 5x2 – 7x = -1 .16, 1.24 -3, 5 . Chapter 10 Solve the equation. 2x2 – 20 = 0 x2 – 2x = 15 5x2 – 7x = -1 3.16, -3.16 -3, 5 . .16, 1.24

. Chapter 10 Linear, Quadratic, or Exponential Function? Linear X 1 2 -1 1 2 Y 4 Quadratic X 1 2 3 Y 6 9 12 Linear . X 1 2 3 4 Y 8 Exponential