What is the foci y=-45x^2-27x+2 ?

The foci y=-45x^2-27x+2 is (-3/10 , 272/45)

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foci y=-45x^2-27x+2

foci

y = - 45 x^{2} - 27 x + 2

(- \frac{3}{10}, \frac{272}{45})

Solution steps

Rewrite

y = - 45 x^{2} - 27 x + 2

in the standard form

4 (- \frac{1}{180}) (y - \frac{121}{20}) = (x - (- \frac{3}{10}))^{2}

(h, k) = (- \frac{3}{10}, \frac{121}{20}), p = - \frac{1}{180}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(- \frac{3}{10}, \frac{121}{20})

along the y-axis

(- \frac{3}{10}, \frac{121}{20} + p)

= (- \frac{3}{10}, \frac{121}{20} + (- \frac{1}{180}))

Refine

(- \frac{3}{10}, \frac{272}{45})

(x - 1)^{2} + 5

y = x^{2} + 4

y = x^{2} - 4

9 x^{2} + 24 x + 16

y = - x^{2} - 4 x - 2