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

The directrix y=+x^2-3 is y=-13/4

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directrix y=+x^2-3

directrix

y = + x^{2} - 3

y = - \frac{13}{4}

Solution steps

Rewrite

y = x^{2} - 3

in the standard form:

4 \cdot \frac{1}{4} (y - (- 3)) = (x - 0)^{2}

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

(0, - 3)

y-coordinate

y = - 3 - p

y = - 3 - \frac{1}{4}

Refine

y = - \frac{13}{4}

x^{2} - 26 x + 65

y^{2} + 2 y + 1 = - 2 x + 4

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

y = x^{2} - 6 x + 5

2 x^{2} - 19 x + 9