What is the directrix y=-(x-4)^2+1 ?

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

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directrix y=-(x-4)^2+1

directrix

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

y = \frac{5}{4}

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (4, 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

(4, 1)

y-coordinate

y = 1 - p

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

Refine

y = \frac{5}{4}

- 12 y + 10 = x^{2} - 4 x + 14

- 2 x^{2} + 11

y = (x - 4) (x - 7)

y = - 2 x^{2} + 6

y = - 2 x^{2} + 7