Question

Determine an equation for a function with the following table of values.Xу142103428540

Answer 1

x | y | first difference | second difference

1 | 4 | |

2 | 10 | 6 = 10 - 4 |

3 | 18 | 8 = 18 - 10 | 2 = 8 - 6

4 | 28 | 10 = 28 - 18 | 2 = 10 - 8

5 | 40 | 12 = 40 - 28 | 2 = 12 - 10

Given that the first differences are not equal, then the equation is not a line

Given that the second differences are equal, then the equation is a quadratic function.

Therefore, the function can be modeled by the next equation:

$y=ax^2+bx+c$

where a, b, and c are some coefficients.

With the help of software, we get:

Rounding c to zero, the obtained equation is:

$y=x^2+3x$