Tell whether the function is quadratic. . {(-2, 0), (-1, 2), (0, 3), (1, 4), (2, 6)}

Question

i dont really understand how to figure out the answer

Answer 1

The x coordinates are all spaced by 1 unit. The gradients between each successive point are:

2, 1, 1, 2 (just the difference between successive y coordinates)

The second gradients are -1, 0, 1.

Let's compare with a simple quadratic: y=ax²+bx+c.

Let's use the same x coordinates from -2 to 2 and calculate the y coordinates:

(-2,4a-2b+c), (-1,a-b+c), (0,c), (1,a+b+c), (4a+2b+c).

First gradients are: -3a+b, -a+b, a+b, 3a+b.

Second gradients are: 2a, 2a, 2a (a constant).

So the given points are not from a quadratic function.