What is the directrix 4x^2+3x-1 ?

The directrix 4x^2+3x-1 is y=-13/8

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directrix 4x^2+3x-1

directrix

4 x^{2} + 3 x - 1

y = - \frac{13}{8}

Solution steps

Rewrite

y = 4 x^{2} + 3 x - 1

in the standard form

4 \cdot \frac{1}{16} (y - (- \frac{25}{16})) = (x - (- \frac{3}{8}))^{2}

(h, k) = (- \frac{3}{8}, - \frac{25}{16}), 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{3}{8}, - \frac{25}{16})

y-coordinate

y = - \frac{25}{16} - p

y = - \frac{25}{16} - \frac{1}{16}

Refine

y = - \frac{13}{8}

x^{2} + a

y = - \frac{1}{4} (x^{2} - 14 x + 13)

x^{2} + 5

y^{2} = - 32 x

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