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.