Question

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HW5.4: Problem 10 Previous Problem Problem List Next Problem point Pre quadratic function of the form f(1) = 0 + ++ car to the data points (0,1),(1,9), (2,-5),(3,-1), using least squares FO)

Answer 1

for least square ATAX* = A'B
solve this for getting

10) $f(t)=4.17-2.5t+0.16t^{2}$

11)

i have attached the detailed solution in the image below.

llo) |(1) - Co + C, +1, = 9 110): 60 +26, +46, 3-5 Fis) = 0+36, +96, --1 L 39 J? UN AXB AX = B is inconsistent ATAX"- AT B . Sot So least square ATAT 4 6 14 16 14 36 114 36 98 o 23 Ol 49 124 O1 2 3 0149 *** BB 38 46.14 * 61436 14 3 6 98 4C6 +677 14- 4 - 0 * * 1/4 t 36 C - - - Z 14 Cor360+986--10 - - L & - 1pcot apc + spc = 0 TM C + 2 c tích - 6 0 (6 C++++)-(+c+ 2 ) :-10 (146* +360+980.)- (2466 +8660546)=-447 * 50+156, -10 -1006–146=-44 15.0+2622 IS=] [45+3(= -2] :56 - 240399 4.17 X = 12 (6*=4.17) (0*5-2.5) (6,*-0.16) (t)= 4.17 - 2.5t +0.16+? 2 -2.5 L 1

Tio Tool 1.5 3.5 f (t) = lote, Sin (t) + C, Coolt) flo) = Cot(, = 1.5 r Fe)-(07c, = 3.5: linolta ( (a) = Co 44C) = 5.5 10.- -OJI +(99) - 60-6, -5.5 5.5 beast squaw LaTax“. AB ATA-riiicrioll 54007 Tirollo Duo LOTO-1 To 02 T10-10 Li-Io. 3.51 Tolo-|| 1010 5.5 * 4 %* p 16 -|C^= > 2C* --2 > 10,* = -1 2 6 * = -4 16 * = -2 14oore 02011 Loo? Le L -4 *) - por n - so - 24 |-|