What is the directrix 4x^2-5x+6 ?

The directrix 4x^2-5x+6 is y= 35/8

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directrix 4x^2-5x+6

directrix

4 x^{2} - 5 x + 6

y = \frac{35}{8}

Solution steps

Rewrite

y = 4 x^{2} - 5 x + 6

in the standard form

4 \cdot \frac{1}{16} (y - \frac{71}{16}) = (x - \frac{5}{8})^{2}

(h, k) = (\frac{5}{8}, \frac{71}{16}), 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{5}{8}, \frac{71}{16})

y-coordinate

y = \frac{71}{16} - p

y = \frac{71}{16} - \frac{1}{16}

Refine

y = \frac{35}{8}

3 x^{2} + x - 5

(y - 0)^{2} = - 4 \cdot 0.01 (x - 0)

3 x^{2} - 10 x + 3

2 y^{2} + 8 x = 0

(x - 2)^{2} = 4 (y + 2)