7. graph the data in the table below. which kind of function best models the data? write an equation to model the data. x y 0 0 1 – 2 2 0 3 6 4 16 linear; y = – 2x quadratic; y = 2x2 – 4x quadratic; y = 2x2 + 4x – 3 exponential; y = 2•4x

You have five points:
A (0 , 0)
B (1 , -2)
C (2 , 0)
D (3 , 6)
E (4 , 16)

Plot these points in a Cartesian plane (see picture attached).

You can deduct what is the correct from the graph, you can see that it is not a linear nor an exponential equation. Indeed, parabolic curves indicate a quadratic function.

Since the graph passes through the point (0, 0), the corresponding function must have a constant term equal to zero.

Therefore the correct answer is: quadratic; y = 2x² – 4x

As a proof, you can substitute the coordinates of your points to see if they belong to this function (and they do).