What is the directrix y=x^2+6x+8 ?

The directrix y=x^2+6x+8 is y=-5/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix y=x^2+6x+8

directrix

y = x^{2} + 6 x + 8

y = - \frac{5}{4}

Solution steps

Rewrite

y = x^{2} + 6 x + 8

in the standard form

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

(h, k) = (- 3, - 1), 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

(- 3, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{5}{4}

- 5 t^{2} + 20 t

y = - (x - 2)^{2} + 4

y^{2} - 2 y - 12 x + 25 = 0

y^{2} - 6 x - y + 11 = 0

4 (x + 1)^{2}