What is the directrix x^2+5x-14 ?

The directrix x^2+5x-14 is y=-41/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix x^2+5x-14

directrix

x^{2} + 5 x - 14

y = - \frac{41}{2}

Solution steps

Rewrite

y = x^{2} + 5 x - 14

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{81}{4})) = (x - (- \frac{5}{2}))^{2}

(h, k) = (- \frac{5}{2}, - \frac{81}{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{5}{2}, - \frac{81}{4})

y-coordinate

y = - \frac{81}{4} - p

y = - \frac{81}{4} - \frac{1}{4}

Refine

y = - \frac{41}{2}

(x - 2) = 3 (y - 5)^{2}

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

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

y = 4 x^{2}

y = 4 x^{2} - 4 x^{1}