At what points do the graphs of y=2x+1 and y=-(x-1)^2+3 intersect?

The question is basically asking when do the two equations equal the same thing
2x +1 = -(x-1)^2+3

move the x's all on one side, and the numbers on the other
2x + (x - 1)^2 = +2

multiply out the brackets:
(x - 1)^2
(x - 1)(x -1)
x^2 -2x +1

put that into the equation instead of the brackets:
2x +x^2 -2x +1 = +2

keep all the x's on one side again:
2x +x^2 -2x = 1

The 2x's cancel out, so:
x^2 = +1

square root:
x = √1 = 1

if x = 1 then put that into the equations to find the value of y when they cross:
y=2x+1
y=2(1)+1
y= 2+1 = 3
y = 3

y= -(x-1)^2 +3
y = -((1) -1)^2 +3 = 3
y = 3

so the point where they cross is (1,3).
I think.
not 100% sure 

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8