What is the foci y=2.1+4.4x-0.7x^2 ?

The foci y=2.1+4.4x-0.7x^2 is (3.14285…,8.65714…)

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foci y=2.1+4.4x-0.7x^2

foci

y = 2.1 + 4.4 x - 0.7 x^{2}

(3.14285 \dots, 8.65714 \dots)

Solution steps

Rewrite

y = 2.1 + 4.4 x - 0.7 x^{2}

in the standard form

4 (- 0.35714 \dots) (y - 9.01428 \dots) = (x - 3.14285 \dots)^{2}

(h, k) = (3.14285 \dots, 9.01428 \dots), p = - 0.35714 \dots

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

p

from the center

(3.14285 \dots, 9.01428 \dots)

along the y-axis

(3.14285 \dots, 9.01428 \dots + p)

= (3.14285 \dots, 9.01428 \dots + (- 0.35714 \dots))

Refine

(3.14285 \dots, 8.65714 \dots)

y = x^{2} - 10 x - 4

(x - 2)^{2} = 8 (y + 1)

x^{2} + 2

5 x^{2} + 210 x - 34775

x^{2} = - 28 y

What is the foci y=2.1+4.4x-0.7x^2 ?
The foci y=2.1+4.4x-0.7x^2 is (3.14285…,8.65714…)