Question

A vertical parabola goes through (1,-2), (-3, 10), and (4, 31). Use matrices to

solve for D, E, and F, given the general form x² + y2 + Dc + Ey + F = 0 (since it

is a vertical parabola there is not a z term).

22.

2 +

Y +

0

Answer 1

D = 1/2 , E = -1/2 , F = -5/2

Explanation:

vertical parabola : ( 1,-2), ( -3, 10 ), (4, 31 )

General form ;
`x^2 + y^2 + Dx + Ey + F = 0`

( 1 ,-2 ) = x1, y1

( -3, 10 ) = x2, y2

( 4, 31 ) = x3, y3

hence :

`y1 = ax_(1) ^2 + bx_(1) + c`

`y2 = ax_(2) ^2 + bx_(2) + c`

`y3 = ax_(3) ^2 + bx_(3) + c`

attached below is the detailed solution required

D = 1/2 , E = -1/2 , F = -5/2