Question 752927
Graph function using the techinique of shifting, compressing, strecthing and /or reflecting
 f(x)=5(x+4)^2+1
<pre>
One important thing to remember in these problems is that 
we must shift vertically UP or DOWN last.

We start with

y = x<sup>2</sup>
{{{graph(200,200,-7.5,2.5,-5,5,x^2)}}}

Then we stretch it vertically by a factor of 5 by multiplying
the right side by 5 and we get

y = 5x<sup>2</sup>
{{{graph(200,200,-7.5,2.5,-5,5,5x^2)}}}

Then we shift it horizontally to the left four units by 
replacing x by (x+4) in the right side and we get:

y = 5(x+4)<sup>2</sup>
{{{graph(200,200,-7.5,2.5,-5,5,5(x+4)^2)}}}

Then finally we shift it vertically up by 1 unit by adding 1 
to the right side.:

y = 5(x+4)<sup>2</sup>+1
{{{graph(200,200,-7.5,2.5,-5,5,5(x+4)^2+1)}}}

And that is the graph of

f(x) = 5(x+4)<sup>2</sup>+1

Edwin</pre>