Two things:

1. The construct (.+|) will match one or more of any character (".+")or nothing ("|)"). So if no value is given there, the regex will match on nothing and return that into $a. Nothing in this case is the empty string, which is not equivalent to undef. To test for this you could test for truth instead of definedness (if($a)), but it'd be much better to specify the fact that $a is optional with the explicit "?", i.e. (.+)? instead of (.+|). The same goes for the other places where you use "|)".
2. Don't use the variables $a and $b like this, they are special variables (see perldoc perlvar) and you can run into strange errors when using them (or at least make your code hard to understand and maintain).

Update: Check out bobfs excellent node True or False? A quick Reference Guide for more on this.

my ($vorzeichen_a_form,$a_form,$vorzeichen_b_seit,$b_seit,$vorzeichen_c_yab, $c_yab) = ($formel =~ m/y=

(+\-)? #$vorzeichen_a_form
(.+)? #$a_form
x\^2 #x^2
(+\-.+)? #$vorzeichen_b_seit, $b_seit
(+\-.+)? #$vorzeichen_c_yab, $c_yab
$/x);

it should work on these combinations:
y=x^2 #no a, b,c
y=-x^2

y=1x^2 #no b,c
y=-1x^2

y=x^2-2 #no b
y=-1x^2-2
y=1x^2-2

y=x^2-2x #no c
y=-1x^2-2x
y=1x^2-2x

y=x^2-2x-2 #a,b, and c are present
y=-1x^2-2x-2
y=1x^2-2x-2

ofcourse, positive values are possible
and ofcourse my idea doesnt work :(

I second hollis suggestion, but here's a regex that does this anyway:

while($formel=<DATA>) {
    my ($vorzeichen_a_form,
        $a_form,
        $vorzeichen_b_seit,
        $b_seit,
        $vorzeichen_c_yab,
        $c_yab) = $formel
            =~ m/y\s*=\s*
               ([-+])?      #$vorzeichen_a_form
               (\d+)?       #$a_form
               x\^2\s*
               (?:             # non-capturing parentheses
                  ([-+])?      #$vorzeichen_b_seit
                  (\d+)?       #$b_seit
                  x\s*
                )?             # make this part optional
                (?:
                  ([-+])?      #$vorzeichen_c_yab
                  (\d+)?       #$c_yab
                )?
               /x;
    print join(":",($vorzeichen_a_form,
                    $a_form,
                    $vorzeichen_b_seit,
                    $b_seit,
                    $vorzeichen_c_yab,
                    $c_yab))."\n";
}

__DATA__
y=x^2 #no a, b,c
y=-x^2
y=1x^2 #no b,c
y=-1x^2
y=x^2-2 #no b
y=-1x^2-2
y=1x^2-2
y=x^2-2x #no c
y=-1x^2-2x
y=1x^2-2x
y=x^2-2x-2 #a,b, and c are present
y=-1x^2-2x-2
y=1x^2-2x-2
[download]


A computer is a state machine. Threads are for people who can't program state machines. -- Alan Cox

use strict;
use warnings;

use Data::Dumper;
use Math::Expr;

my $e=Parse("y=ax^2+bx+c");

print Dumper ($e);
[download]

$VAR1 = bless( {
 'Breakable' => 0,
 'Val' => '=',
 'Opps' => [
   bless( {
    'Val' => 'y',
    'VarType' => 'Real'
   }, 'Math::Expr::Var' ),
   bless( {
    'Breakable' => 1,
    'Val' => '+',
    'Opps' => [
      bless( {
       'Breakable' => 1,
       'Val' => '+',
       'Opps' => [
        bless( {
         'Breakable' => 1,
         'Val' => '^',
         'Opps' => [
          bless( {
            'Val' => 'ax',
            'VarType' => 'Real'
          }, 'Math::Expr::Var' ),
          bless( {
            'Val' => '2'
          }, 'Math::Expr::Num' )
          ]
        }, 'Math::Expr::Opp' ),
        bless( {
         'Val' => 'bx',
         'VarType' => 'Real'
        }, 'Math::Expr::Var' )
       ]
      }, 'Math::Expr::Opp' ),
      bless( {
       'Val' => 'c',
       'VarType' => 'Real'
      }, 'Math::Expr::Var' )
     ]
   }, 'Math::Expr::Opp' )
  ]
 }, 'Math::Expr::Opp' );
[download]

the for your replys, have to test that.

If you want to check if it matched a 0-length string, try
if (length($a))

Altogether, it can be written as:
$a = 1 if not length $a;
or
$a = 1 if length $a != 0;

By the way, you shouldn't use $a and $b as variables. They mean something special to sort.

What breaks if he escapes it? Nothing

Except it causes confusion for future maintainers. "Why did he escape the question mark? Is that something I haven't learned before? Is this why I'm getting a bug, or should I look somewhere else?"

Always try to reduce confusion for future maintainers.

    -Bryan