If the points in the table lie on a parabola, write the equation whose graph is the parabola. x|-3 |-2 |-1 |0 y|-1 |-4 |-1 |8

Given the table of points that lie on a parabola.



The equation of a parabola is given by , where a, b and c are constants. Since the equation of a data point has three constants, three data points/equations will be needed to obtain the value of the constants and hence the required equation.

when x = 0, y = 8 and we have:


When x = -1, y = -1 and we have:



When x = -2, y = -4 and we have:



Solving the two equations simultaneously, we have:



Thus, a = 3, b = 12 and c = 8

Therefore, the required equation of the parabola is given by: