What is the directrix-x^2+5x+6 ?

The directrix-x^2+5x+6 is y= 25/2

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directrix-x^2+5x+6

directrix

- x^{2} + 5 x + 6

y = \frac{25}{2}

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - \frac{49}{4}) = (x - \frac{5}{2})^{2}

(h, k) = (\frac{5}{2}, \frac{49}{4}), 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

(\frac{5}{2}, \frac{49}{4})

y-coordinate

y = \frac{49}{4} - p

y = \frac{49}{4} - (- \frac{1}{4})

Refine

y = \frac{25}{2}

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

5 x + 3 y^{2} = 0

+ (x - 1)^{2} + 2

3 - 4 x^{2}

2 y^{2} - 5 y + x - 4 = 0