What is the directrix 0.5x^2+2 ?

The directrix 0.5x^2+2 is y= 3/2

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directrix 0.5x^2+2

directrix

0.5 x^{2} + 2

y = \frac{3}{2}

Solution steps

Rewrite

y = 0.5 x^{2} + 2

in the standard form:

4 \cdot \frac{1}{2} (y - 2) = (x - 0)^{2}

(h, k) = (0, 2), p = \frac{1}{2}

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

(0, 2)

y-coordinate

y = 2 - p

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

Refine

y = \frac{3}{2}

y = - 2 + x^{2}

y^{2} + 4 x + 1 = 0

5 x^{2} - 13 x - 6

x^{2} - 4 x - 5

4 x^{2} + 12 x + 9