leitkurve (4x^3-7x^2-11x+5)/(4x+5)

Lösung

leitkurve

\frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

y = - \frac{3}{2}

Schritte zur Lösung

Rewrite

y = \frac{4 x ^{3} - 7 x ^{2} - 11 x + 5}{4 x + 5}

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{5}{4})) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - \frac{5}{4}), p = \frac{1}{4}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(\frac{3}{2}, - \frac{5}{4})

y-coordinate

y = - \frac{5}{4} - p

y = - \frac{5}{4} - \frac{1}{4}

Fasse zusammen

y = - \frac{3}{2}

d i rec t r i x (\frac{1}{2} - x) (- \frac{1}{2} - x)

d i rec t r i x y = - 8 x^{2}

d i rec t r i x 3 x^{2} - x

d i rec t r i x x^{2} + 14 x + 46

d i rec t r i x - 3 x^{2} + 17 x - 20