Two forms for finding the equation

When we have to reconstruct the equation of a parabola from some data, it is convenient to choose the form best suited to the information we have.

Observation — Two ways to find the equation of a parabola

Depending on the known data one starts from different forms of the equation:

• if you know the intersections with the $x$-axis, that is $x_A$ and $x_B$: $y=a(x-x_A)(x-x_B)$;
• if you know the vertex $V(x_V,y_V)$: $y-y_V=a(x-x_V)^2$.

In both cases a further point is needed to determine the coefficient $a$.

Two equivalent strategies for writing the equation of a parabola, depending on the available data.

Links

Topics: Parabola
Concepts: Parabola · Vertex
Functions: Parabola
Skills: Analytic geometry · Using formulae