What is the directrix y= 1/2 (x^2-4x+2) ?

The directrix y= 1/2 (x^2-4x+2) is y=-3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

directrix y= 1/2 (x^2-4x+2)

directrix

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

y = - \frac{3}{2}

Solution steps

Rewrite

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

in the standard form

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

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

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}{2}

Refine

y = - \frac{3}{2}

4 x^{2} - 6 x - 2

4 x^{2} + 16 x - 3

x = 2 y^{2} - 1 - (5 y - 6)

x^{2} - 2 x - 4 y + 13 = 0

y = 18 x^{2} - 14 x + 9

What is the directrix y= 1/2 (x^2-4x+2) ?
The directrix y= 1/2 (x^2-4x+2) is y=-3/2