What is the directrix 7x^2-5x+9 ?

The directrix 7x^2-5x+9 is y= 113/14

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directrix 7x^2-5x+9

directrix

7 x^{2} - 5 x + 9

y = \frac{113}{14}

Solution steps

Rewrite

y = 7 x^{2} - 5 x + 9

in the standard form

4 \cdot \frac{1}{28} (y - \frac{227}{28}) = (x - \frac{5}{14})^{2}

(h, k) = (\frac{5}{14}, \frac{227}{28}), p = \frac{1}{28}

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}{14}, \frac{227}{28})

y-coordinate

y = \frac{227}{28} - p

y = \frac{227}{28} - \frac{1}{28}

Refine

y = \frac{113}{14}

- 8 x^{2} + 4 x

3 y + 4 x = - 2 x^{2} - 14

- x^{2} - 6 x - 13

3 x^{2} - 6 x + 9

2.6 + 2.2 x - 0.6 x^{2}