Question

how do i find all solutions to the system y=-x squared-4x+12 and y=-2x+4

Answer 1

u can set them equal to eachother, that's one way u can go at it
-x^2 -4x+12=-2x+4 (move stuff over)
-x^2-4x+12+2x-4=0 (add 2x, subtract 4 from both sides)
-x^2-2x+8=0 (combine like terms)
x^2+2x-8=0 (it makes it easier to take out the negative sign infront of the x^2)
factor the eqn and u get (x+4)(x-2)
to find the individual x values, set each part equal to 0
x+4=0, x-2=0
so ur x values would be x=-4, 2