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

The directrix x^2+3x+4 is y= 3/2

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directrix x^2+3x+4

directrix

x^{2} + 3 x + 4

y = \frac{3}{2}

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{4} (y - \frac{7}{4}) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, \frac{7}{4}), p = \frac{1}{4}

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}{2}, \frac{7}{4})

y-coordinate

y = \frac{7}{4} - p

y = \frac{7}{4} - \frac{1}{4}

Refine

y = \frac{3}{2}

y^{2} = - x

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

y = - 12 x^{2} - 29 x + 230

y = x^{2} - 5 x 3

y = (x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})