Question 912790
You can move the parabola either right
or left by writing equation as:
{{{ y = ( x - a )^2 }}}
{{{ y = x^2 - 2ax + a^2 }}}
-------------------
Notice that {{{ y = 0 }}} when
{{{ 0 = ( a - a )^2 }}}
The vertex is at (a,0)
------------------
This is how you move the vertex from
(0,0) to anywhere on the x-axis
-----------------------------
Then, in order to move up or down,
you need:
{{{ y = ( x-a )^2 + b }}}
----------------------
To make the parabola narrower ( skinny ),
{{{ y = c*( x-a )^2 + b }}}
where {{{ c>1 }}}
To make the parabola wider ( fatter ),
{{{ c <1 }}}
------------
Say
 {{{ a = 3 }}}
{{{ b = 5 }}}
{{{ c = 1 }}}
---------------
A 2nd parabola is:
{{{ a = 3 }}}
{{{ b = -5 }}}
{{{ c = 4 }}}
Here are the plots:
{{{ graph( 400, 400, -3, 10, -7, 10, ( x - 3 )^2 - 5, 4*( x - 3 )^2 - 5 ) }}}
The skinnier one is:
{{{ y = 4*( x-3 )^2 - 5 }}}
Hope this helps