IB: Matrix quadratic equation help?

Question

hi , i am in huge trouble so please help me through this question.

If you explain it , it would be even better! i have a table:

Speed (kmh-1) (y) Braking distance (m) (X)

32 ...........................................

48.......................................

64.......................................

80.......................................

96.......................................

112......................................

how can i create a function of this data (Speed vs braking distance) using qudratic matrix function method.. and please write the function by showing steps..

It actually a IB maths portfolio.. so if somebody has done eariler, can you please tell me how you did ?

Thanks a lot, i will definetly give you the best answer for this.

sorry in the table i miss the braking distance data

here it is in respect to the speed:

6

14

24

38

55

75

Answer 1

If you want to model the data with a 2nd order polynomial (y = a +  bx + cx²), the equation to solve, in matrix form, to get optimal values for a, b, and c is:

| 6 432 35584 ....................... | | a |  = | 212  |

| 432 35584 3207168 ........... | | b |  = | 19120 |

| 35584 3207168 306380800 | | c |  = | 1827584  |

a= 0.6

b = -0.023214286

c = 0.006138393

Answer: y = 0.006138393x² - 0.023214286x + 0.6

You can examine the derivation of a least-squares parabola fit at efunda.com