What is the directrix 1/3 x^2-8/3 x+1/3 ?

The directrix 1/3 x^2-8/3 x+1/3 is y=-23/4

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directrix 1/3 x^2-8/3 x+1/3

directrix

\frac{1}{3} x^{2} - \frac{8}{3} x + \frac{1}{3}

y = - \frac{23}{4}

Solution steps

Rewrite

y = \frac{1}{3} x^{2} - \frac{8}{3} x + \frac{1}{3}

in the standard form

4 \cdot \frac{3}{4} (y - (- 5)) = (x - 4)^{2}

(h, k) = (4, - 5), p = \frac{3}{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, - 5)

y-coordinate

y = - 5 - p

y = - 5 - \frac{3}{4}

Refine

y = - \frac{23}{4}

2 x^{2} - 7 x + 15

3 x^{2} - 12 x + 5

18 x^{2} - 6 x + 4

x^{2} - 4 x - y + 3 = 0

y = - 3 (x - 2) (x + 5)

What is the directrix 1/3 x^2-8/3 x+1/3 ?
The directrix 1/3 x^2-8/3 x+1/3 is y=-23/4