What is the directrix y=(x-2)^2-7 ?

The directrix y=(x-2)^2-7 is y=-29/4

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directrix y=(x-2)^2-7

directrix

y = (x - 2)^{2} - 7

y = - \frac{29}{4}

Solution steps

Rewrite

y = (x - 2)^{2} - 7

in the standard form:

4 \cdot \frac{1}{4} (y - (- 7)) = (x - 2)^{2}

(h, k) = (2, - 7), 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

(2, - 7)

y-coordinate

y = - 7 - p

y = - 7 - \frac{1}{4}

Refine

y = - \frac{29}{4}

y > x^{2} - 3

x^{2} + 20 y = 10

2 y^{2} = - 3 x

x^{2} + 8 x + 7

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