What is the directrix 4x^2+10x-10 ?

The directrix 4x^2+10x-10 is y=-261/16

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directrix 4x^2+10x-10

directrix

4 x^{2} + 10 x - 10

y = - \frac{261}{16}

Solution steps

Rewrite

y = 4 x^{2} + 10 x - 10

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{65}{4})) = (x - (- \frac{5}{4}))^{2}

(h, k) = (- \frac{5}{4}, - \frac{65}{4}), 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

(- \frac{5}{4}, - \frac{65}{4})

y-coordinate

y = - \frac{65}{4} - p

y = - \frac{65}{4} - \frac{1}{16}

Refine

y = - \frac{261}{16}

(x - 7)^{2} = - 12 (y - 1)

y^{2} = 5 y + 7 x + 3

2 y^{2} - 12 y - x + 5 = 0

- 0.03 x^{2} + 45 x + 124.5

- x^{2} - 4 x