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
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