Algebra II
posted by Anonymous .
How many real solutions does the function shown on the graph have?
a) no real solutions
b) one real solution
c) two real solutions
d) cannot be determined
___________________________
y = (x+2)^2 + 3 is shown on the graph.
I am having trouble figuring this one out. I have been looking in my book for a while now. Somebody please help, it would be very much appreciated!

Algebra II 
Anonymous
I think it could be a) no real solutions?
Am I correct? If not, please explain... 
Algebra II 
Anonymous
Whoops. I meant the graph was showing: y=(x+2)^2+2

Algebra II 
Anonymous
I was thinking that it is a) because it does not have any xintercepts?

Algebra II 
Bosnian
( x + 2 )² + 2 = 0
Subtract 2 to both sides
( x + 2 )² + 2  2 = 0  2
( x + 2 )²=  2
Take square root of both sides
x + 2 = ± √(  2 )
x + 2 = ± √(  1 ∙ 2 )
x + 2 = ±√(  1 ) ∙ √2
x + 2 = ± i √2
Subtract 2 to both sides
x + 2  2 = ± i √2  2
x =  2 ± i √2
The solutions are:
x =  2 + i √2 and x =  2  i √2
The function ( x + 2 )² + 2 no real solutions.
Answer a) is correct 
Algebra II 
Reiny
Just looking at the equation, we can tell that the vertex is (2,2) and the parabola opens upwards. So clearly, it cannot cross the xaxis. So clearly, no real solution
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1. How many real solutions does the function shown on the graph have?