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

The directrix x^2-5x+6 is y=-1/2

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directrix x^2-5x+6

directrix

x^{2} - 5 x + 6

y = - \frac{1}{2}

Solution steps

Rewrite

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

in the standard form

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

(h, k) = (\frac{5}{2}, - \frac{1}{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{1}{4})

y-coordinate

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

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

Refine

y = - \frac{1}{2}

y = (x - 4)^{2}

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

9 t - 2 t^{2}

x^{2} = 40 y

x^{2} - 6 x - y + 33 = 0