What is the directrix y=3.1+6.6x-2.3x^2 ?

The directrix y=3.1+6.6x-2.3x^2 is y=7.94347…

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directrix y=3.1+6.6x-2.3x^2

directrix

y = 3.1 + 6.6 x - 2.3 x^{2}

y = 7.94347 \dots

Solution steps

Rewrite

y = 3.1 + 6.6 x - 2.3 x^{2}

in the standard form

4 (- 0.10869 \dots) (y - 7.83478 \dots) = (x - 1.43478 \dots)^{2}

(h, k) = (1.43478 \dots, 7.83478 \dots), p = - 0.10869 \dots

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

(1.43478 \dots, 7.83478 \dots)

y-coordinate

y = 7.83478 \dots - p

y = 7.83478 \dots - (- 0.10869 \dots)

Refine

y = 7.94347 \dots

y = 3 x^{2} 4

- 7 x^{2}

x^{2} - x - 2

2 x^{2} + 5 x - 7

10 y^{2} = 22 x

What is the directrix y=3.1+6.6x-2.3x^2 ?
The directrix y=3.1+6.6x-2.3x^2 is y=7.94347…