Find the quadratic function that is best fit for f(x)

vakirnarhh 2021-12-03 Answered
Find the quadratic function that is best fit for f(x) defined by the table below
Xf(x)0024014159863595864071010,009
The quadratic function is y=.
(Type an equation using as the variable. Round to two decimals places as needed)
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Expert Answer

Ralph Lester
Answered 2021-12-04 Author has 16 answers

Step 1
Let the quadratic equation be
f(x)=ax2+bx+c
Since there are 3 unknowns a, b, c.
Let us use the least square method for the curve fit
Step 2
xyxyx2x2yx3x400000002401802416048164159863921625568642566359521570361294202161296864075125664410048512409610100091000901001000900100010000x=30y=22010xy=180110x2=220x2y=1567540x3=1800x4=15664
Step 3
number of data =n=6
Step 2
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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