What is the directrix y=x^2+4x+3 ?

The directrix y=x^2+4x+3 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+4x+3

directrix

y = x^{2} + 4 x + 3

y = - \frac{5}{4}

Solution steps

Rewrite

y = x^{2} + 4 x + 3

in the standard form

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

(h, k) = (- 2, - 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

(- 2, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{5}{4}

3 x^{2} + 5 x - 4

y = - x^{2} - 1

+ 6 x^{2} + 6 x - 12

y^{2} = 20 (x - 10)

y = 3 x^{2} - 18 x + 23