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

luipieduq3

luipieduq3

Answered question

2021-12-03

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)15264778119
Table B
x01234g(x)1526374859
linear function =
quadratic function =

Answer & Explanation

Befory

Befory

Beginner2021-12-04Added 19 answers

Step 1
Table A
xf(x)first differencesecond difference015111261021247103137810414119
Table B
xf(x)2615015111261124711378114119
In table B first difference between two terms =11. So, given table B is linear function model.
So,Equation of linear function:
g(x)=y=11x+15
Answer:
Equationg(x)=11x+15
Table BLinear Model
Step 2
In table A second difference between two terms is 10, so given table A is quadratic function model.
So, equation of quadratic function:
y=ax2+bx+c
At point (x, y)=(0, 15)
15=a(0)2+b(0)+c
Step 3
At point (x, y)=(1, 26)
26=a(1)2+b(1)+c
a+b+c=26
a+b=26c (c=15)
a+b=2615
1) a+b=11
At point (x, y)=(2, 47)
47=a(2)2+b(2)+c
47=4a+26+15
4a+2b=32
2) 2a+b=16
Step 4
Solve equation (1) and (2)
a=5
a+b=11
b=115
b=6
quadratic form f(x)=y=ax2+bx+c
=5x2+6x+15
Answer: Equation
f(x)=5x2+6x+15
Table A quadratic model

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