Suppose it is a quadratic function, the equation is y=ax²+bx+c use the first three points to find a, b, and c (0, -3): -3=0a+0b+c, c=-3 (1,-2): -2=a+b-3 =>a+b=1 (2,1); 1=4a+2b-3 =>4a+2b=4 solve for a and b, we get a=1, b=0
so the quadratic equation is y=x²-3
Next, find out if the other two points fit this equation. when x=3, y=3²-3=6, so (3,6) works. when x=4, y=4²-3=13, so (4,13) also fits this equation.
yes, all these points are on the graph. This is a quadratic function.
