Question 716715
{{{ y = a*x^2 + b*x + c  }}}
is the general equation for a parabola.
It can either look like a cup that is holding
water ( open up ), or a cup that is 
upside down ( open down )
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The sign of {{{ a }}} tells which it is.
To make it simple, suppose {{{ b = 0 }}} and {{{ c = 0 }}}
Then you have
{{{ y = ax^2 }}}
Suppose {{{ a = 3 }}} ( cup holding water )
Suppose {{{ a = -3 }}} ( cup upside down )
Here is a graph of both these cases:
{{{ graph( 400, 400, -5, 5, -5, 5, 3x^2, -3x^2 ) }}}
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The value of {{{ a}}} determines how fat or skinny 
the cup is. large {{{ a }}}, skinny cup, and
small {{{ a }}}, fat cup
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The numbers you pick for {{{ b }}} and {{{ c }}}
doesn't change these basic rules. They just move the
graph around the x-y plane.
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Suppose I compare:
{{{ y = 3x^2 + 4x - 1 }}} and
{{{ y = -3x^2 + 4x - 1 }}}
You can see they just moved relative to where the vertexes
were at the origin.
{{{ graph( 400, 400, -5, 5, -5, 5, 3x^2 + 4x - 1, -3x^2 + 4x - 1 ) }}}
Hope this helps