What is the directrix y=4x^2+5 ?

The directrix y=4x^2+5 is y= 79/16

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directrix y=4x^2+5

directrix

y = 4 x^{2} + 5

y = \frac{79}{16}

Solution steps

Rewrite

y = 4 x^{2} + 5

in the standard form:

4 \cdot \frac{1}{16} (y - 5) = (x - 0)^{2}

(h, k) = (0, 5), p = \frac{1}{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

(0, 5)

y-coordinate

y = 5 - p

y = 5 - \frac{1}{16}

Refine

y = \frac{79}{16}

(x + 4)^{2} - 3

x^{2} + 12 x + 6 y + 10 = 0

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

(x - 3) (x - 7)

- (x - 1)^{2} + 5