y = -x + 7
y = 0.5(x - 3)^2
Set the y's equal
0.5( x - 3)^2 = - x + 7 to make this easier, multiply through by 2....this gets rid of the "0.5"
(x - 3)^2 = -2x + 14 simplify
x^2 - 6x + 9 = -2x + 14 rearrange as
x^2 - 4x - 5 = 0 factor
(x - 5) ( x + 1) = 0
Setting each factor to 0 and solving for x produces
x = 5 or x = - 1
And using y = - x + 7
When x = 5, y = -5 + 7 = 2
When x = -1, y = -(-1 ) + 7 = 8
So.....the solutions are ( 5, 2) and ( -1. 8)