This week in Pre-Calculus 11 we learned about equivalent forms of the quadratic functions, analyzing , and applying what we learned this unit into word problems. This post I am going to focus in on equivalent forms of the quadratic functions. There are three equivalent forms of the quadratic function the general, standard, and factored form. We are going to look on the general and standard form.

General form —> 

Standard form —>

When changing between general and standard form you have to use the completing the square method to do so.

This week in Pre-Calculus 11 we learned about quadratic functions. We learned about the properties, looking at an equation and extracting information for the parabola, and analyzing $latexy=a(x-p)^2+q$. I am going to focus on looking at an equation and extracting information for the parabola. Translations can go up and down or side to side. Scales can either stretch or compress the parabola.

$latexy=x^2+p$ —> The parabola moves up/down because there are no brackets around $latexy=x^2+p$

$latexy=(x-p)^2$ —> The parabola moves left or right because there are brackets around x-p. When p is negative the parabola moves to the right but if p is positive the parabola moves to the left.

$larexy=ax^2$ —> The parabola stretches when a is greater than 1. If a is less than one the parabola compresses. Also if a is negative the parabola will open down instead of up.