Answer
quadratic
Explanation
When you graph the set of points (picture 1), you realize that the first and fourth points have the same y-coordinate and the x-coordinate of the fourth point is the x-coordinate of the first point multiplied by -1. The same also applies for the second and third points. This is the typical behavior of a quadratic graph. Remember that the quadratic function is always symmetric about a line, so every point will have a reflection about that line. Since (2, 10 ) is a reflection of the point (-2, 10) about the y-axis and the same can be said of (1, 1) and (-1, 1), we can conclude that our model is quadratic.
You can rule out a linear model because no straight line pass through (or near) all points. You can also rule out an exponential model because the function is decreasing and then increasing; exponential models either grow (increase) or decay.
As bonus, the equation of the quadratic graph that model the situation is: [tex]f(x)=\frac{5}{2} x^2[/tex]
