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Finite Differences

Finite Differences. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Updated 12-5-08. Determine the degree of the function given the set of finite differences. 1 st. 2 nd. Now, identify the function of degree 2. 3.

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Finite Differences

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  1. Finite Differences By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Updated 12-5-08

  2. Determine the degree of the function given the set of finite differences. 1st 2nd

  3. Now, identify the function of degree 2. 3 For a 2nd degreefunction, how manypoints do we need to write the equation? f(x) = ax2 + bx + c f(1) = a(1)2 + b(1) + c = 1a + 1b + c = 0 f(2) = a(2)2 + b(2) + c = 4a + 2b + c = 13 f(3) = a(3)2 + b(3) + c = 9a + 3b + c = 6 We will use this system to solve for a, b, & c.

  4. Now, identify the function of degree 2. f(x) = ax2 + bx + c f(1) = a(1)2 + b(1) + c = 1a + 1b + c = 0 f(2) = a(2)2 + b(2) + c = 4a + 2b + c = 13 RREF f(3) = a(3)2 + b(3) + c = 9a + 3b + c = 6 f(x) = ax2 + bx + c a = 3 b = 4 f(x) = 3x2 + 4x - 7 c = -7

  5. Determine the degree of the function given the set of finite differences. 1st 2nd 3rd 4th

  6. Now, identify the function of degree 4. 5 For a 4th degreefunction, how manypoints do we need towrite the equation? f(x) = ax4 + bx3 + cx2 + dx + e f(1) = 1a + 1b + 1c + 1d + e = -4 f(2) = 16a + 8b + 4c + 2d + e = -7 f(3) = 81a + 27b + 9c + 3d + e = 38 f(4) = 256a + 64b + 16c + 4d + e = 227 f(5) = 625a + 125b + 25c + 5d + e = 704 We will use this system to solve for a, b, & c.

  7. Solve the system: 1a + 1b + 1c + 1d + e = -4 16a + 8b + 4c + 2d + e = -7 81a + 27b + 9c + 3d + e = 38 RREF 256a + 64b + 16c + 4d + e = 227 625a + 125b + 25c + 5d + e = 704 a = 2 f(x) = ax4 + bx3 + cx2 + dx + e b = -4 c = -2 f(x) = 2x4 – 4x3 – 2x2 + x – 1 d = 1 e = -1

  8. Determine the degree of the function 4, 7, 10, 13, 16, 19, 22, 25, 28 3, 3, 3, 3, 3, 3, 3, 3 1st difference 1st Degree Jeff Bivin -- LZHS

  9. Now, write the linear model 1st Degree f(1) f(2) 4, 7, 10, 13, 16, 19, 22, 25, 28 (1, 4) (2, 7) Jeff Bivin -- LZHS

  10. Determine the degreeof the function -1, 0, 5, 14, 27, 44, 65, 90, 119 1, 5, 9, 13, 17, 21, 25, 29 1st difference 4, 4, 4, 4, 4, 4, 4 2nd difference 2nd Degree Jeff Bivin -- LZHS

  11. Now write the quadratic model 2nd Degree f(1) f(2) f(3) -1, 0, 5, 14, 27, 44, 65, 90, 119 Solve the system Jeff Bivin -- LZHS

  12. Now write the quadratic model 2nd Degree f(1) f(2) f(3) -1, 0, 5, 14, 27, 44, 65, 90, 119 a = 2 b = -5 c = 2 Jeff Bivin -- LZHS

  13. Determine the degreeof the function 1, 10, 47, 130, 277, 506, 835, 1282, 1865 9, 37, 83, 147, 229, 329, 447, 583 1st difference 28, 46, 64, 82, 100, 118, 136 2nd difference 3rd Degree 18, 18, 18, 18, 18, 18 3rd difference Jeff Bivin -- LZHS

  14. Now write the quadratic model 3rd Degree f(1) f(2) f(3) f(4) 1, 10, 47, 130, 277, 506, 835, 1282, 1865 Solve the system Jeff Bivin -- LZHS

  15. Now write the quadratic model 3rd Degree f(1) f(2) f(3) f(4) 1, 10, 47, 130, 277, 506, 835, 1282, 1865 a = 3 b = -4 c = 0 d = 2

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