Zum Inhalt springen

Lösung Formen von Parabelgleichungen

Zuletzt geändert von Martin Rathgeb am 2025/01/07 23:33

Teillösung.

Nr. Hauptform Scheitelform Produktform
1 y = x^2 - 4x + 3 y = (x - 2)^2 - 1 y = (x - 1)(x - 3)
2 y = x^2 + 2x + 5 y = (x + 1)^2 + 4  
3 y = x^2 + 4x + 4 y = (x + 2)^2 y = (x + 2)(x + 2)
4 y = -(x^2 - 4x + 1) y = -(x - 2)^2 + 3 y = -(x - (2 - \sqrt{3}))(x - (2 + \sqrt{3}))
5 y = -\pi x^2 + 2\pi x - \pi y = -\pi(x - \pi)^2 + \pi^2 y = -\pi(x - 1)(x - 3)
6 y = -x^2 - 2x - 1 y = -(x + 1)^2 - 2 y = -(x + 1 - \sqrt{2})(x + 1 + \sqrt{2})
7 y = 2x^2 + 4x + 10 y = 2(x + 1)^2 + 8 y = 2(x + 2 - \sqrt{2})(x + 2 + \sqrt{2})
8 y = -\frac{3}{2}(x^2 - 4x + 4) y = -\frac{3}{2}(x - 2)^2 y = -\frac{3}{2}(x - 2)(x - 2)
9 y = \sqrt{2}x^2 - 5\sqrt{2}x + 6\sqrt{2} y = \sqrt{2}(x - \frac{5}{2})^2 - \frac{1}{4} y = \sqrt{2}(x - 2)(x - 3)