What is the directrix y=-4(x-2)^2+16 ?

The directrix y=-4(x-2)^2+16 is y= 257/16

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix y=-4(x-2)^2+16

directrix

y = - 4 (x - 2)^{2} + 16

y = \frac{257}{16}

Solution steps

Rewrite

y = - 4 (x - 2)^{2} + 16

in the standard form:

4 (- \frac{1}{16}) (y - 16) = (x - 2)^{2}

(h, k) = (2, 16), p = - \frac{1}{16}

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, 16)

y-coordinate

y = 16 - p

y = 16 - (- \frac{1}{16})

Refine

y = \frac{257}{16}

4 X^{2} + 12 X + 9

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

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

- (y + 3)^{2} - 1

7 x^{2} - 3 x + 10 - (- 4 x^{2} + 6 x - 4)

What is the directrix y=-4(x-2)^2+16 ?
The directrix y=-4(x-2)^2+16 is y= 257/16