What is the directrix y=-0.5x^2-3 ?

The directrix y=-0.5x^2-3 is y=-2.5

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directrix y=-0.5x^2-3

directrix

y = - 0.5 x^{2} - 3

y = - 2.5

Solution steps

Rewrite

y = - 0.5 x^{2} - 3

in the standard form:

4 (- 0.5) (y - (- 3)) = (x - 0)^{2}

(h, k) = (0, - 3), p = - 0.5

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

(0, - 3)

y-coordinate

y = - 3 - p

y = - 3 - (- 0.5)

Refine

y = - 2.5

4 x^{2} + 48 y + 12 x = 159

(x - 3)^{2} = - 8 (y + 2)

4 x^{2} - 2 x

y = - x^{2} + 18 x - 79

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