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Chapter 10 Story Problems

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 = 0.012x 2. Range 0 < y < 12.288. Domain -32 < x < 32 .

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Chapter 10 Story Problems

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  1. Chapter 10 Story Problems Domain x values Range y values

  2. Chapter 10 Story Problems Domain x values Range y values p. 633 #40 Find domain and range y = 0.012x2 Range 0 <y< 12.288 Domain -32<x< 32

  3. Falling Objects - Two acorns drop from an oak tree. One falls 45 feet while the other falls 32 feet. Chapter 10 Story Problems 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).

  4. Falling Objects - A pinecone falls about 25 feet from the branch of the tree. How long does it take to land on the ground? Chapter 10 Story Problems 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?

  5. 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? Chapter 10 Story Problems 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?

  6. 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? Chapter 10 Story Problems Graph the equation. What are looking for? Vertex? X-intercept? . Use the 2nd Calc key to solve. About 66 feet

  7. 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? Chapter 10 Story Problems Graph the equation. What are looking for? Vertex? X-intercept? . Use the 2nd Calc key to solve. About 66 feet

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

  9. y = 5x2 + 3x + 12 Minimum Graph upward Chapter 10 Minimum or Maximum? Maximum Graph downward y = -3x2 - 7x + 15 Minimum Graph upward y = x2 - 5x + 6 y = -8x2 + 10x - 20 Maximum Graph downward . y = 4x2 - 5x - 25 Minimum Graph upward

  10. X = 0 Axis of symmetry Vertex Min or Max Opens Up or Down y = -4x2 - 3 (0, -3) Max No Solutions Chapter 10.1/2 Review 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

  11. 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. Chapter 10 Story Problems Graph the equation. What are looking for? Vertex? X-intercept? . h = -16t2 + vt + s About 1.7 sec

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

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

  14. Linear, Quadratic, or Exponential Function? Chapter 10 Quadratic Linear . Exponential

  15. X = 0 Axis of symmetry Vertex Min or Max Opens Up or Down y = 3x2 + 4 (0, 4) Min No Solutions Chapter 10.1/2 Review 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

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

  17. Linear, Quadratic, or Exponential Function? Chapter 10 Quadratic Linear . Exponential

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