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

kloseyq

kloseyq

Answered question

2021-12-09

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)053023.410015414.6402205638.6892442
The function f(x) is   quadratic, and h(x) is   quadratic.

Answer & Explanation

Buck Henry

Buck Henry

Beginner2021-12-10Added 33 answers

Step 1
For f(x) first and second differences are,
53.414.638.61.611.22412.812.8
As the second differences are exactly equal, hence f(x) is exactly quadratic.
Step 2
For g(x) first and second differences are,
3100402892103302490199188
As the second differences are nearly equal, hence g(x) is approximately quadratic.
Step 3
For h(x) first and second differences are,
0152054421519023717547
As there is a large difference between second differences, hence h(x) is not quadratic.

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