In how many ways can you identify the equation of this parabola?
In Name that graph we thought about the three formats in which we can write a quadratic equation. We explored some of the ways in which the equation of a parabola could be determined in each of these three forms and the relative efficiency of each.
Here we have three coordinates specified on the parabola, but because the graph is not plotted accurately with a background grid, we cannot read any additional points from the diagram.
We could of course go through the laborious process of forming three equations, one from each of the specified points on the parabola, in \(a,b, c\) and solve them simultaneously. This will give an equation in the form \(y=ax^2+bx+c\).
We could instead locate the line of symmetry and use this to find the equation of the parabola in completed square form.
Making use of the diagram in “Have you thought about…” we could find the equation by considering a translation of the original parabola.