What is the directrix 3x^2+19x-40 ?

The directrix 3x^2+19x-40 is y=-421/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix 3x^2+19x-40

directrix

3 x^{2} + 19 x - 40

y = - \frac{421}{6}

Solution steps

Rewrite

y = 3 x^{2} + 19 x - 40

in the standard form

4 \cdot \frac{1}{12} (y - (- \frac{841}{12})) = (x - (- \frac{19}{6}))^{2}

(h, k) = (- \frac{19}{6}, - \frac{841}{12}), p = \frac{1}{12}

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{19}{6}, - \frac{841}{12})

y-coordinate

y = - \frac{841}{12} - p

y = - \frac{841}{12} - \frac{1}{12}

Refine

y = - \frac{421}{6}

(y - 10)^{2} = - 12 (x + 2)

x^{2} + 4 x - 8 y + 12 = 0

x^{(2)} - 6 x + 5 y = - 34

12 (y - 2) = (x + 2)^{2}

x^{2} - 3 x - 4