One of the things we learned this week in Precalc 11 is the equivalent forms of the equation of a quadratic function. There are three main forms we write quadratic functions in, standard/vertex form, factored form, and the general form.

The standard form or the vertex form is probably the most helpful one since it gives us information about the coordinates of the vertex and the amount it stretches or compresses.

The factored form gives us information about the x-intercepts and the amount it stretches or compresses.

The general form is probably the least helpful one since it only gives us information about the y-intercept and whether it opens up or down. However, the general form can be easily converted to the standard/vertex form by completing the square and to the factored form by factoring the trinomial

How to convert the equivalent forms

We always want to start with the general form when converting equations, since when converting to standard/vertex form we have to complete the square and we can’t do that with the factored form unless we convert the factored form to the general form and same when converting to factored form, we have to convert the standard/vertex form to the general form first.

General to Standard/Vertex

General to Factored