What is the directrix y=2x^2+6x+10 ?

The directrix y=2x^2+6x+10 is y= 43/8

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directrix y=2x^2+6x+10

directrix

y = 2 x^{2} + 6 x + 10

y = \frac{43}{8}

Solution steps

Rewrite

y = 2 x^{2} + 6 x + 10

in the standard form

4 \cdot \frac{1}{8} (y - \frac{11}{2}) = (x - (- \frac{3}{2}))^{2}

(h, k) = (- \frac{3}{2}, \frac{11}{2}), 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

(- \frac{3}{2}, \frac{11}{2})

y-coordinate

y = \frac{11}{2} - p

y = \frac{11}{2} - \frac{1}{8}

Refine

y = \frac{43}{8}

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

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

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

X^{2} - 5 X - 24

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