What is the directrix x^2+7x+12 ?

The directrix x^2+7x+12 is y=-1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x^2+7x+12

directrix

x^{2} + 7 x + 12

y = - \frac{1}{2}

Solution steps

Rewrite

y = x^{2} + 7 x + 12

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{1}{4})) = (x - (- \frac{7}{2}))^{2}

(h, k) = (- \frac{7}{2}, - \frac{1}{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{7}{2}, - \frac{1}{4})

y-coordinate

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

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

Refine

y = - \frac{1}{2}

- x^{2} + 1

- x^{2} + 7

y = - 16 x^{2} + 16 x + 480

- x^{2} + 5 x - 7

(x - 1)^{2} = 8 (y + 3)