What is the directrix 5x^2-15x+3 ?

The directrix 5x^2-15x+3 is y=-83/10

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directrix 5x^2-15x+3

directrix

5 x^{2} - 15 x + 3

y = - \frac{83}{10}

Solution steps

Rewrite

y = 5 x^{2} - 15 x + 3

in the standard form

4 \cdot \frac{1}{20} (y - (- \frac{33}{4})) = (x - \frac{3}{2})^{2}

(h, k) = (\frac{3}{2}, - \frac{33}{4}), p = \frac{1}{20}

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{33}{4})

y-coordinate

y = - \frac{33}{4} - p

y = - \frac{33}{4} - \frac{1}{20}

Refine

y = - \frac{83}{10}

x^{2} + 10 x - 24

x (4 - x)

5 x^{2} - 3 x + 3

y = (x - 3)^{2} + 4

(x + 4)^{2} = - 12 (y - 2)