What is the directrix-x^2+6x+1 ?

The directrix-x^2+6x+1 is y= 41/4

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directrix-x^2+6x+1

directrix

- x^{2} + 6 x + 1

y = \frac{41}{4}

Solution steps

Rewrite

y = - x^{2} + 6 x + 1

in the standard form

4 (- \frac{1}{4}) (y - 10) = (x - 3)^{2}

(h, k) = (3, 10), 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

(3, 10)

y-coordinate

y = 10 - p

y = 10 - (- \frac{1}{4})

Refine

y = \frac{41}{4}

y = 3 x^{2} + 1 - (x + 4)

x^{2} = 8 (y + 4)

y = 2 x (x - 9) - (x - 9)

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

- x^{2} + 14 x - 45