What is the directrix 7x^2-3x+10-(-4x^2+6x-4) ?

The directrix 7x^2-3x+10-(-4x^2+6x-4) is y= 267/22

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directrix 7x^2-3x+10-(-4x^2+6x-4)

directrix

7 x^{2} - 3 x + 10 - (- 4 x^{2} + 6 x - 4)

y = \frac{267}{22}

Solution steps

Rewrite

y = 7 x^{2} - 3 x + 10 - (- 4 x^{2} + 6 x - 4)

in the standard form

4 \cdot \frac{1}{44} (y - \frac{535}{44}) = (x - \frac{9}{22})^{2}

(h, k) = (\frac{9}{22}, \frac{535}{44}), p = \frac{1}{44}

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{9}{22}, \frac{535}{44})

y-coordinate

y = \frac{535}{44} - p

y = \frac{535}{44} - \frac{1}{44}

Refine

y = \frac{267}{22}

y = - 2 x^{2} + 64 x - 90

y = \frac{1}{2} (x^{2} - 4 x + 2)

4 x^{2} - 6 x - 2

4 x^{2} + 16 x - 3

x = 2 y^{2} - 1 - (5 y - 6)

What is the directrix 7x^2-3x+10-(-4x^2+6x-4) ?
The directrix 7x^2-3x+10-(-4x^2+6x-4) is y= 267/22