How do you write a quadratic equation when given two points?

1 Answer
Apr 21, 2018

Two points are not sufficient to specify a quadratic equation.


Consider a quadratic equation in factored form.


If we specify #r_1# and #r_2#, then we know exactly two points on this parabola, namely #(r_1, 0)#, and #(r_2, 0)#. But there are an infinite number of parabolas that contain these two points because we can make the #a# coefficient any real number.

We need a THIRD point to fix the parabola.

One special circumstance exists, though. Suppose the two points we are given are (1, 4) and (6, 4). Because these points lie on a vertical line, there would be NO parabola that could contain both of these points. In general, if the two points have the same #y#-value, the two points cannot be on the same parabola.