Answer
Quadratic function
Work Step by Step
First, calculate slope of two consecutive ordered pair coordinates:
The coordinates are \[\left( 0,12 \right),\left( 1,3 \right),\left( 2,0 \right),\left( 3,3 \right),\text{ and}\left( 4,12 \right)\].
\[\text{Since, }m=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)\],
Now, calculate slopes of two consecutive ordered pair of coordinates:
\[\begin{align}
& {{m}_{1}}=\left( \frac{3-12}{1-0} \right)=\frac{-9}{1}=-9 \\
& {{m}_{2}}=\left( \frac{0-3}{2-1} \right)=\frac{-3}{1}=-3 \\
& {{m}_{3}}=\left( \frac{3-0}{3-2} \right)=\frac{3}{1}=3 \\
& {{m}_{4}}=\left( \frac{12-3}{4-3} \right)=\frac{9}{1}=9
\end{align}\]
It can be seen that slopes of any two consecutive coordinate pairs are negative, then becomes positive. It is the property of quadratic function.
Therefore, the ordered pair value of this table represents the graph of a quadratic function.
