## Function f

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) |
\(f(x)\) |

1 |
2 |

2 |
6 |

3 |
12 |

4 |
20 |

5 |
30 |

100 |
10,100 |

\(f(x) = x(x+1) = x^2 + x \)

## Function g

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) |
\(g(x)\) |

0 |
0 |

1 |
5 |

2 |
12 |

3 |
21 |

4 |
32 |

137 |
19,317 |

\(g(x) = x(x+4) = x^2 + 4x\)

## Function h

Give a quadratic function that would result in the values given below. Compute the missing value.

\(x\) |
\(h(x)\) |

1 |
-4 |

3 |
1 |

5 |
12 |

7 |
29 |

9 |
52 |

11 |
81 |

141 |
14,836 |

\(h(x) = \frac{3}{4} x^2 - \frac{1}{2} x - \frac{17}{4} \)

## Function j

Give a **linear** function that would result in the values given below.

\(x\) |
\(j(x)\) |

3 |
25 |

4 |
23 |

5 |
21 |

6 |
19 |

7 |
17 |

8 |
15 |

Linear function general form \(ax + b\), answer: \(j(x) = -2 x + 31 \).

## Function k

Unfortunately this method will not always work. Why won't it work in the example below?

\(x\) |
\(k(x)\) |

0 |
1 |

1 |
2 |

2 |
4 |

3 |
8 |

4 |
16 |

5 |
32 |

Differences never become constant. Function is not polynomial but is exponential in this case, \(k(x) = 2^x \).

## Challenge: Function m

Give a polynomial function that would result in the values given below. Compute the missing value.

\(x\) |
\(m(x)\) |

0 |
2 |

1 |
3 |

2 |
6 |

3 |
12 |

4 |
22 |

100 |
171,702 |

\(k(x) = \frac{1}{6} x^3 + \frac{1}{2} x^2 + \frac{1}{3} x + 2\)

## Random quadratic functions

x |
p(x) |

1 |
1 |

2 |
2 |

3 |
4 |

4 |
7 |

5 |
11 |

100 |
4951 |

Coefficient answers for general quadratic: a = 1/2, b = -1/2, c = 1