What is the directrix 2x^2-10 ?

The directrix 2x^2-10 is y=-81/8

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directrix 2x^2-10

directrix

2 x^{2} - 10

y = - \frac{81}{8}

Solution steps

Rewrite

y = 2 x^{2} - 10

in the standard form:

4 \cdot \frac{1}{8} (y - (- 10)) = (x - 0)^{2}

(h, k) = (0, - 10), p = \frac{1}{8}

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, - 10)

y-coordinate

y = - 10 - p

y = - 10 - \frac{1}{8}

Refine

y = - \frac{81}{8}

y^{2} = 4 (- 4) x

(y + 1)^{2} = - 4 (x - 2)

(x - h)^{2} = 4 (- 8) (y - 3)

100 + 6 x^{2} - 8 x

x^{2} - 6 x + 5