Question

Find the intersection points of the parabola y=−x2−2 and the line −x+y=−4.

Answer 1

Answer:

I don't know but I think it is simultaneous equation

Answer 2

Answer:

$y = - {x}^{2} - 2 - - - (i) \\ - x + y = - 4 - - - (ii)$

from equation (ii):

$y = x - 4 - - - (iii)$

substitute y in (i) with y in (iii):

$- {x}^{2} - 2 = x - 4 \\ - {x}^{2} - x + 2 = 0 \\ {x}^{2} + x - 2 = 0 \\ (x - 1)(x + 2) = 0 \\ \\ { \underline{x = 1 \: \: and \: \: - 2}}$

find y:

$y = x - 4 \\ { \underline{y = - 3 \: \: and \: \: - 6}}$

therefore points of intersection:

${ \underline{ \underline{ \boxed{ \boxed{(1, \: - 3) \: \: and \: \: ( - 2, \: - 6)}}}}}$