Answer:
h is the horizontal translation
k is the vertical translation
a is the stretch parallel to the y-axis
Step-by-step explanation:
Parent equation: [tex]y=x^2[/tex]
Translate [tex]h[/tex] units right: [tex]y=(x-h)^2[/tex]
(if [tex]h < 0[/tex], then the translation is [tex]h[/tex] units left)
Stretched parallel to the y-axis by a factor of [tex]a[/tex]: [tex]y=a(x-h)^2[/tex]
(if [tex]a < 0[/tex], the graph is also reflected in the x-axis)
Translated k units up: [tex]y=a(x-h)^2+k[/tex]
(if [tex]k < 0[/tex] then the translation is k units down)
Example attached for [tex]y=2(x-3)^2+4[/tex]
