What is the directrix X^2-5X-24 ?

The directrix X^2-5X-24 is y=-61/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix X^2-5X-24

directrix

X^{2} - 5 X - 24

y = - \frac{61}{2}

Solution steps

Rewrite

y = X^{2} - 5 X - 24

in the standard form

4 \cdot \frac{1}{4} (y - (- \frac{121}{4})) = (X - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, - \frac{121}{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{121}{4})

y-coordinate

y = - \frac{121}{4} - p

y = - \frac{121}{4} - \frac{1}{4}

Refine

y = - \frac{61}{2}

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

y^{2} + 4 y + 8 x - 12 = 0

4 x^{2} - 8 x + 2 y = 5

88 x - 16 x^{2} - 112

- 16 t^{2} + 60 t + 3