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

The directrix y= 1/2 (x+1)^2+4 is y= 7/2

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

directrix

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

y = \frac{7}{2}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (- 1, 4), 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

(- 1, 4)

y-coordinate

y = 4 - p

y = 4 - \frac{1}{2}

Refine

y = \frac{7}{2}

(y - 6)^{2} = 36 (x - 2)

(x - 0)^{2} = 4 y - 4

y = x + x^{2}

4 x - 11 y^{2} = 0

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

What is the directrix y= 1/2 (x+1)^2+4 ?
The directrix y= 1/2 (x+1)^2+4 is y= 7/2