What is the directrix+4x^2-4x+9 ?

The directrix+4x^2-4x+9 is y= 127/16

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directrix+4x^2-4x+9

directrix

+ 4 x^{2} - 4 x + 9

y = \frac{127}{16}

Solution steps

Rewrite

y = 4 x^{2} - 4 x + 9

in the standard form

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

(h, k) = (\frac{1}{2}, 8), 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{1}{2}, 8)

y-coordinate

y = 8 - p

y = 8 - \frac{1}{16}

Refine

y = \frac{127}{16}

x^{2} - 2

4 - (x - 3)^{2}

+ x^{2} - 6 x - 7

lo g_{10} (6) x^{2}

y = \frac{1}{14} x^{2} + 2