leitkurve 5x(2x+4)-3x

Lösung

leitkurve

5 x (2 x + 4) - 3 x

y = - \frac{29}{4}

Schritte zur Lösung

Rewrite

y = 5 x (2 x + 4) - 3 x

in the standard form

4 \cdot \frac{1}{40} (y - (- \frac{289}{40})) = (x - (- \frac{17}{20}))^{2}

(h, k) = (- \frac{17}{20}, - \frac{289}{40}), p = \frac{1}{40}

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{17}{20}, - \frac{289}{40})

y-coordinate

y = - \frac{289}{40} - p

y = - \frac{289}{40} - \frac{1}{40}

Fasse zusammen

y = - \frac{29}{4}

d i rec t r i x x^{2} + 12 y = 0

d i rec t r i x (x - 1)^{2} = - 2 y - 11

d i rec t r i x (x - 2)^{2} = 8 (y + 1)

d i rec t r i x y^{2} = 24 x

d i rec t r i x y = - \frac{( x + 3 ) ^{2}}{20} + 1