What is the directrix y=40x-5x^2 ?

The directrix y=40x-5x^2 is y= 1601/20

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directrix y=40x-5x^2

directrix

y = 40 x - 5 x^{2}

y = \frac{1601}{20}

Solution steps

Rewrite

y = 40 x - 5 x^{2}

in the standard form

4 (- \frac{1}{20}) (y - 80) = (x - 4)^{2}

(h, k) = (4, 80), p = - \frac{1}{20}

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, 80)

y-coordinate

y = 80 - p

y = 80 - (- \frac{1}{20})

Refine

y = \frac{1601}{20}

4 y^{2} + 3 x = 0

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

x^{2} - 4 x + 2

x^{2} - 4 x + 3

y = 3 x - 3 x^{2}