Find the quadratic function that is best fit for f(x) defined by the table below

Josalynn 2020-10-18 Answered

Find the quadratic function that is best fit for f(x) defined by the table below

Xf(x)0024014159863595864071010,009

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Expert Answer

toroztatG
Answered 2020-10-19 Author has 98 answers

Step 1 Let the quadratic equation be f(x)=ax2+bx+c Since there are 3 unlnowns a, b, c Let us use the least square method for the curve fit

Step 2

Xyxyx2x2yx3x400000002401802416048164159863921625568642566359521570361294202161296864075125664410048512409610100091000901001000900100010000x=30y=22010xy=180110x2=220x2y=1567540x3=1800x4=1

Step 3 number of data =n=6 y=ax2+bx+nc
22010=220a+30b+6c.(1)
xy=ax3+bx2+cx
180110=1800a+220b+30c.(2)
x2y=ax4+bx3+cx2
1567540=15664a+1800b+220c.(3) Step 4 Solve equation (1), (2) and (3) a=100.29
b=2.04
c=1.25
y=100.29x22.04x+1.25

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