What is the directrix 3-t^2 ?

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directrix 3-t^2

directrix

3 - t^{2}

y = \frac{13}{4}

Solution steps

Rewrite

y = 3 - t^{2}

in the standard form:

4 (- \frac{1}{4}) (y - 3) = (t - 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}

y = - 8 (x + 1)^{2}

- 8 (y + 1) = (x - 2)^{2}

+ 2 x^{2} + 24 x + 76

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

y^{2} + 2 x = 0