Answer:
h is the horizontal translation
k is the vertical translation
a is the stretch parallel to the y-axis
Explanation:
Parent equation:
![y=x^2](https://img.qammunity.org/2023/formulas/mathematics/college/1ch5n55tacdusoaz2xqjwppl7gqbo47w29.png)
Translate
units right:
![y=(x-h)^2](https://img.qammunity.org/2023/formulas/mathematics/college/uwsam81m3gj8g1b21hmk8kdnfegpd4ge16.png)
(if
, then the translation is
units left)
Stretched parallel to the y-axis by a factor of
:
![y=a(x-h)^2](https://img.qammunity.org/2023/formulas/mathematics/college/q15wsnp4mdhykynpocdgpht98n8zg0fbfo.png)
(if
, the graph is also reflected in the x-axis)
Translated k units up:
![y=a(x-h)^2+k](https://img.qammunity.org/2023/formulas/mathematics/college/97p0xsjs0cwme4ddvwkim2cbbqprhnlhsv.png)
(if
then the translation is k units down)
Example attached for
![y=2(x-3)^2+4](https://img.qammunity.org/2023/formulas/mathematics/college/udi61ftr13obcny3whu9fbqsuqbm325v1o.png)