What is the directrix y=(-4x^2+24x+161)/(25) ?

The directrix y=(-4x^2+24x+161)/(25) is y= 3777/400

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directrix y=(-4x^2+24x+161)/(25)

directrix

y = \frac{- 4 x ^{2} + 24 x + 161}{25}

y = \frac{3777}{400}

Solution steps

Rewrite

y = \frac{- 4 x ^{2} + 24 x + 161}{25}

in the standard form

4 (- \frac{25}{16}) (y - \frac{197}{25}) = (x - 3)^{2}

(h, k) = (3, \frac{197}{25}), p = - \frac{25}{16}

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, \frac{197}{25})

y-coordinate

y = \frac{197}{25} - p

y = \frac{197}{25} - (- \frac{25}{16})

Refine

y = \frac{3777}{400}

x^{2} - 12 x + 35

x = (2 y + 5)^{2}

6 x^{2} - 12 x

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

y = (x + 1)^{2} + 5

What is the directrix y=(-4x^2+24x+161)/(25) ?
The directrix y=(-4x^2+24x+161)/(25) is y= 3777/400