What is the foci y=(-3x^2-2x+6)/5 ?

The foci y=(-3x^2-2x+6)/5 is (-1/3 , 17/20)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci y=(-3x^2-2x+6)/5

foci

y = \frac{- 3 x ^{2} - 2 x + 6}{5}

(- \frac{1}{3}, \frac{17}{20})

Solution steps

Rewrite

y = \frac{- 3 x ^{2} - 2 x + 6}{5}

in the standard form

4 (- \frac{5}{12}) (y - \frac{19}{15}) = (x - (- \frac{1}{3}))^{2}

(h, k) = (- \frac{1}{3}, \frac{19}{15}), p = - \frac{5}{12}

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

p

from the center

(- \frac{1}{3}, \frac{19}{15})

along the y-axis

(- \frac{1}{3}, \frac{19}{15} + p)

= (- \frac{1}{3}, \frac{19}{15} + (- \frac{5}{12}))

Refine

(- \frac{1}{3}, \frac{17}{20})

y = x^{2} + 2 x + 3

x^{2} = - 10 y

y = 3 x^{2} + 5 x - 4

x^{2} - 4 x + 4

y = - 144 x^{2} - 192 x - 48