Question

Which two points satisfy y = -x2 + 2x + 4 and x + y = 4?

Answer 1

lets graph it first

where they intersect is where our 2 points will satisfy

Answer 2

let x = 0
y= ?
here it satisfys one point (x,y) or (0,?)

Answer 3

x + y = 4
4-x = y subtracting x both sides

4-x = - x2 + 2x + 4 ----substituting 4-x for y
-x = -x2 + 2x subtracting 4 both sides
0 = -x2 + 3x adding x
0 = -x(x-3) factoring -x out


let both equal zero by Zero Product Property

x-3=0 (x,y) so (3,?) substitute back in

we already have our zero for x from before