Question 1145166
Transform the function f(x) as described and write the resulting function as an equation

f(x)=x^2
 Translate left 2 units
stretch horizontally by a factor of 2
reflect over the x-axis
stretch vertically by a factor of 3
translate up 4 units
<pre>
Start with 

{{{f(x)=x^2}}} <--the red graph

{{{graph(400,400,-10,10,-10,10,x^2)}}}

</pre>Translate left 2 units<pre>

replace x by (x+2)

{{{g(x) = (x+2)^2}}} <--the green graph

{{{graph(400,400,-10,10,-10,10,x^2,(x+2)^2)}}}

</pre>stretch horizontally by a factor of 2<pre>

Replace x by x/2

{{{h(x) = (x/2+2)^2}}} <--the blue graph

{{{graph(400,400,-10,10,-10,10,x^2,(x+2)^2,(x/2+2)^2)}}}

</pre>reflect over the x-axis<pre>

Multiply the whole right side by -1

{{{k(x)=-(x/2+2)^2}}} <--the purple graph (it opens downward)

{{{graph(400,400,-10,10,-10,10,x^2,(x+2)^2,(x/2+2)^2,-(x/2+2)^2)}}}

</pre>stretch vertically by a factor of 3<pre>

Multiply the whole right side by 3.

{{{m(x)=-3(x/2+2)^2}}} <---the yelowish-green graph (opens downward)

{{{graph(400,400,-10,10,-10,10,x^2,(x+2)^2,(x/2+2)^2,-(x/2+2)^2,-3(x/2+2)^2))}}}

</pre>translate up 4 units<pre>

Add +4 to the whole right side:

{{{m(x)=-3(x/2+2)^2+4}}} <---the light blue graph.

{{{graph(400,400,-10,10,-10,10,x^2,(x+2)^2,(x/2+2)^2,-(x/2+2)^2,-3(x/2+2)^2,4-3(x/2+2)^2))}}}

Edwin</pre>