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

The directrix y=x^2+4x-3 is y=-29/4

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{29}{4}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (- 2, - 7), 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, - 7)

y-coordinate

y = - 7 - p

y = - 7 - \frac{1}{4}

Refine

y = - \frac{29}{4}

y = 18 x^{2} - 6 x + 4

7 x^{2} - 7 x

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

y = (x + 3) (x - 1)

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