One of the two tables below shows data that can best be modeled by a l

f480forever2rz

f480forever2rz

Answered question

2021-12-04

One of the two tables below shows data that can best be modeled by a linear function, and the other shows data that can best be modeled by a quadratic function. Identify which table shows the linear data and which table shows the quadratic data, and find a formula for each model.
Table A
x01234f(x)8214271108
Table B
x01234g(x)821344760
linear function =
quadratic function =

Answer & Explanation

Thouturs

Thouturs

Beginner2021-12-05Added 12 answers

Step 1
Given Table A
xf(x)=yx2x3x4x×yx2y080000012111121212424816841683719278121363941081664256432172810250301003547502556
y=a+bx+cx2 quadratic equation normal equation are
y=an+bx+cx2
xy=ax+bx2+cx3
x2y=ax2+bx3+cx4
Substituting there value in above equation
1) 5a+106+30c=250
2) 10a+306+100c=750
3) 30a+100b+354c=2556
(1)×2(2)
4) 10640c=250
(1)×6(3)
5) 40b174c=1056
(4)×4(5)
14c=56
c=4
From (3)
10b40c=250
10b160=250
Step 2
b=9010=9
From (1)
5a+90+120=250
5a=40
a=8
Put a, b, and c in quadratic equation we get
f(x)=y=8+9x+4x2
b) Given Table B
xg(x)=yx2x×y080012112124246837191414108162401025030470
Straight line equation y=a+bx normal equation are
y=an+bx

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