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Term 2 grade 11 core project

Term 2 grade 11 core project. The polynomial project. Done by : alreem Adel and moza ganhm. Class: 11.53. Task 1 : find the polynomial that gives the foll ow ing values. P(x)= A+B(x-x0)+C(x-x1) + D(x-x0)(x-x1)(x-x2)

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Term 2 grade 11 core project

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  1. Term 2 grade 11 core project The polynomial project Done by : alreem Adel and moza ganhm Class: 11.53

  2. Task 1 : find the polynomial that gives the following values P(x)= A+B(x-x0)+C(x-x1) + D(x-x0)(x-x1)(x-x2) Write the system of equation in A.B.C and D that you can use to find the desired polynomial. 10=A -6+A+B(x2-x0) + C (x3-x0)(x2-x1) 82= A+B (x3-x0) + C (x3 – x0)(x3 – x0 ) (x3-x0) (x3-x4) (x3-x2)

  3. B. solve the system obtained from part A. 10 =A -6=10+B(-1(-1)) 2B=-16 B=-8 -17=10+8(2-(-1)) +C (2-1-) +C ((2(-1)) (2-(-1)) 3 = c=-3 82=10+-8(5-(-1))+-1(5-(_1)(5-1)+D(5-(-1))(5-1)(5-2) 72D=144 D=2 A=10 B=-1 C=-1 D=2

  4. c. find the polynomial t that represent the four ordered Paris. P(x)=10+-8(x-(-1)) + -1(x-1(-1)) (x-1) +2(x-(-1)) (x-1) (x-2) =10-8x-8-x2+1(2))(x3-2x2-x+2) =3-x2-8x+2x3-4x2-2x+4 =2x3-5x2-10+7

  5. D. write the general form of the polynomial of degree 4 for 5 pairs of number. P(x)=A+B(x-x0) + C(x-x0) C(x-x0)(x-x1)+p(x-x0) (x-x1)(x-x2)+E(x-x0)(x-x1)(x-x2)(x-x3) =Ex4+(2-7E)x3+(9E-5)x2+(7E-10)x+(7-10E)

  6. Task2”:find the zero of the polynomial found in task1 • A. show that the zeros of the polynomial found in task1 are: • First zero lies between -2 and -1 • Second lies between 0 and 1 • Third zero lies between 3 and 4 F(-2)=1f(-1)=10 midpoint = -1.5 F(0)=7f(1)=-6 0.5 F(3)=-14,f(4)=15 3.5

  7. B. find to the nearest tenth the third zero using the bisection method for approximate real zeros.

  8. Task 3:real world construction. • You are planning a rectangular garden. Its length is twice its width. You want a walkway w feet wide around the garden. Let x be the width of the garden. • A. choose any value for the width of the walkway w that is less than 6 ft. w=1ft b. Write an expression for the area of the garden and walk. A=f x w =2wxw A=2x2ft2 Parameter= 2(ftw) =2(2x+x) Parameter=6x

  9. C. write an expression for the area of the walkway only. Parameter =2 (f +w) =2 (2w +w) =2(3w) =6x ft

  10. You have enough gravel to cover 1000ft2 and want to use it all on the walk. How big should you make the garden? 1000=2w2 1000=2x2 500=x2 22.36ft=x F=2x =2x22.36 F=44.72ft

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