Can you please explain the transformations involved when transforming y = x^2 to y = 4(3x -6)^2 + 1
Hello, elmidge!
$\displaystyle \text{Can you please explain the transformations involved}$
$\displaystyle \text{when transforming }\,y \:=\: x^2\,\text{ to }\,y\:=\:4(3x -6)^2 + 1$
$\displaystyle \text{We are going from }\,y \:=\:x^2\,\text{ to }\,y \:=\:36(x-2)^2 + 1$
$\displaystyle \text{I assume you know the graph of: }\:y \,=\,x^2.$
$\displaystyle \text{We have: }\:y \:=\:(x\,{\color{red}-\,2})^2$
. . $\displaystyle \text{The graph is moved 2 units to the right.}$
$\displaystyle \text{Then: }\:y \:=\:{\color{red}36}(x-2)^2$
. . The graph is stretched vertically by a factor of 36.
$\displaystyle \text{Finally: }\:y \:=\:36(x-2)^2\, {\color{red}+ 1}$
. . The graph is moved one unit upward.
The vertex of $\displaystyle y = x^2$ is at $\displaystyle (0,0)$
The vertex of $\displaystyle y = (x + p)^2 + q $ is at $\displaystyle (- p, q)$. A translation p units in the negative x direction and q units in the positive y.
If you complete the square for $\displaystyle y = 9x^2 - 6x$, you will have it in the above, vertex, form and will therefore know the transformations involved.
Can you do that?