The points follow quadratic equation model.
Explanation:
To find the model, we can find the slope of the points.
Slope of two points = [tex]\frac{y_2 - y_1}{x_2 - x_!}[/tex]
The given points are: (-2, 10), (-1, 1), (1, 1), (2, 10)
[tex]slope 1 = \frac{1 - 10}{-1 + 2} = -9[/tex]
[tex]slope 2 = \frac{1 -1}{1 + 1} = 0\\\\slope 3 = \frac{10 - 1}{2 - 1} = 9[/tex]
We can rule out a linear model because no straight line pass through (or near) all points and also the slope of the points are not same.
We can also rule out an exponential model because the function is decreasing and then increasing; exponential models either grow (increase) or decay.
The graph drawn follows the function [tex]f(x) = \frac{5}{2} x^2[/tex]
Therefore, it is a quadratic equation.
