leitkurve y=5x^2+6x-7

Lösung

leitkurve

y = 5 x^{2} + 6 x - 7

y = - \frac{177}{20}

Schritte zur Lösung

Rewrite

y = 5 x^{2} + 6 x - 7

in the standard form

4 \cdot \frac{1}{20} (y - (- \frac{44}{5})) = (x - (- \frac{3}{5}))^{2}

(h, k) = (- \frac{3}{5}, - \frac{44}{5}), p = \frac{1}{20}

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}{5}, - \frac{44}{5})

y-coordinate

y = - \frac{44}{5} - p

y = - \frac{44}{5} - \frac{1}{20}

Fasse zusammen

y = - \frac{177}{20}

d i rec t r i x (x - 1)^{2} = - 6 (y + 4)

d i rec t r i x 7 x^{2} + 70 x + 178

d i rec t r i x x^{2} - 6 x - 28 y = - 93

d i rec t r i x x^{2} + 17 x + 16

d i rec t r i x y = (x + 1) (x + 2)