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

The foci y=3x^2-6x+5 is (1, 25/12)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

foci y=3x^2-6x+5

foci

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

(1, \frac{25}{12})

Solution steps

Rewrite

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

in the standard form

4 \cdot \frac{1}{12} (y - 2) = (x - 1)^{2}

(h, k) = (1, 2), p = \frac{1}{12}

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

p

from the center

(1, 2)

along the y-axis

(1, 2 + p)

= (1, 2 + \frac{1}{12})

Refine

(1, \frac{25}{12})

2 x^{2} - 12 x - 5

(x - 5) (x - 3)

(y - 2) (y + 5)

x^{2} - 4 x + 24

(x - 5)^{2} = - 70 (y - 1)