The table to the right has the​ inputs, x, and the outputs for three​

ArcactCatmedeq8

ArcactCatmedeq8

Answered question

2021-11-30

The table to the right has the​ inputs, x, and the outputs for three​ functions, f,​ g, and h. Use second differences to determine which function is exactly​ quadratic, which is approximately​ quadratic, and which is not quadratic.
Xf(x)g(x)h(x)042026.411811421.6462152649.61017343
The function f(x) is   quadratic, and h(x) is   quadratic.

Answer & Explanation

Sharolyn Larson

Sharolyn Larson

Beginner2021-12-01Added 12 answers

Step 1
Given,
The table to the right has the​ inputs, x, and the outputs for three​ functions, f,​ g, and h.
xf(x)g(x)h(x)042026.411811421.6462152649.61017343
Step 2
for the f(x)
xf(x)First differencesecond difference0426.46.44=2.4421.621.66.4=15.215.22.4=12.8649.649.621.6=282815.2=12.8
If the second difference is the same value, the model will be quadratic.
therefore, function f (x) is exactly quadratic.
Step 3
for the g(x)
xg(x)First differencesecond difference022118118(2)=1204462462118=344344120=224610171017462=555555344=211
therefore, function g(x) is not quadratic.
Step 4
for the h(x)
xh(x)First differencesecond difference00211110=11415215211=14114111=1306343343152=191191141=50
therefore, function h(x) is not quadratic.

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