What is the foci-0.2t^2+1.6t+98.4 ?

The foci-0.2t^2+1.6t+98.4 is (4,100.35)

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foci-0.2t^2+1.6t+98.4

foci

- 0.2 t^{2} + 1.6 t + 98.4

(4, 100.35)

Solution steps

Rewrite

y = - 0.2 t^{2} + 1.6 t + 98.4

in the standard form

4 (- 1.25) (y - 101.6) = (t - 4)^{2}

(h, k) = (4, 101.6), p = - 1.25

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

p

from the center

(4, 101.6)

along the y-axis

(4, 101.6 + p)

= (4, 101.6 + (- 1.25))

Refine

(4, 100.35)

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

- y^{2} = 6 y + x

(y + 1)^{2} = 16 (x - 3)

(x + 1) (x - 5)

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