What is the directrix y=x^2+x+3 ?

The directrix y=x^2+x+3 is y= 5/2

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directrix y=x^2+x+3

directrix

y = x^{2} + x + 3

y = \frac{5}{2}

Solution steps

Rewrite

y = x^{2} + x + 3

in the standard form

4 \cdot \frac{1}{4} (y - \frac{11}{4}) = (x - (- \frac{1}{2}))^{2}

(h, k) = (- \frac{1}{2}, \frac{11}{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{1}{2}, \frac{11}{4})

y-coordinate

y = \frac{11}{4} - p

y = \frac{11}{4} - \frac{1}{4}

Refine

y = \frac{5}{2}

- 2 x = (y + 3)^{2} + 6

y = \frac{3 x ^{3} - 6 x ^{2}}{x - 2}

- 3 x^{2} + 6 x - 1

(x + 6)^{2} = - 20 (y - 5)

\frac{x ^{3}}{x}