When graphing quadratics, there are ways to change the positions of a point (x , y). When dealing with a quadratic and transitions, it is important to convert the equation into vertex form.
y = a(x-h)2+k
Note: The vertex of the parabola (h , k).
Translations:
(h , _)
Left when h < 0
Right when h > 0
(_ , k)
Down when k < 0
Up when k > 0
Example Problem 1:
g(x) = (x2+4x)-12 translated to f(x) = -1((x2+4x)-12) -10
(Click To Enlarge Image)
Notice: There are points along the blue dashed equation to show how you can apply the translations to different points and create the equation in bold red. Also, using the axis of symmetry, you can use one point to calculate the distance of another.
