What is the directrix 5y=-(x-3)^2-25 ?

The directrix 5y=-(x-3)^2-25 is y=-15/4

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directrix 5y=-(x-3)^2-25

directrix

5 y = - (x - 3)^{2} - 25

y = - \frac{15}{4}

Solution steps

Rewrite

5 y = - (x - 3)^{2} - 25

in the standard form:

4 (- \frac{5}{4}) (y - (- 5)) = (x - 3)^{2}

(h, k) = (3, - 5), p = - \frac{5}{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

(3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - (- \frac{5}{4})

Refine

y = - \frac{15}{4}

x^{2} + 2 x

y = x^{2} - 8 x + 10

y = x^{2} + 12 x + 45

y = (5 x - 8)^{2}

y = 5 x^{2} + 6 x - 7