What is the directrix y=48x-8x^2 ?

The directrix y=48x-8x^2 is y= 2305/32

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directrix y=48x-8x^2

directrix

y = 48 x - 8 x^{2}

y = \frac{2305}{32}

Solution steps

Rewrite

y = 48 x - 8 x^{2}

in the standard form

4 (- \frac{1}{32}) (y - 72) = (x - 3)^{2}

(h, k) = (3, 72), p = - \frac{1}{32}

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, 72)

y-coordinate

y = 72 - p

y = 72 - (- \frac{1}{32})

Refine

y = \frac{2305}{32}

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

y = - 2 x^{2}

y = 2 x^{2} - 3

(y + 1)^{2} = 16 (x - 3)

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