What is the directrix (x-5)^2-1 ?

The directrix (x-5)^2-1 is y=-5/4

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directrix (x-5)^2-1

directrix

(x - 5)^{2} - 1

y = - \frac{5}{4}

Solution steps

Rewrite

y = (x - 5)^{2} - 1

in the standard form:

4 \cdot \frac{1}{4} (y - (- 1)) = (x - 5)^{2}

(h, k) = (5, - 1), 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

(5, - 1)

y-coordinate

y = - 1 - p

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

Refine

y = - \frac{5}{4}

- 2 x^{2} + 4 x - 2

- x^{2} + 150 x - 2000

(x 2 + 1)^{2}

y = (x + 2) (x - 3)

y = + 3 x^{2} + 24 x - 51