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!

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

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

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 
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
Respond to this Question
Similar Questions

Math
I am given 4 choices for the problem the square root of 8x 2 = the square root of 2x. The choices are a)x=2 or 2/9 b)no solutions c)2/9 or d)x=2.I have imput the numbers and gotten a variety of solutions none of which are any of the … 
Algebra
For the following equation, state the value of the discriminant and then describe the nature of the solutions. 7x^2+3x4=0 What is the value of the disriminant? 
algebra
determine the nature of the solutions of the equation, one real solution, two real solutions, or two nonreal solutions. x^220x+100=0 
algebra
determine the nature of the solutions of the equation. Two real solutions, two imaginary solutions, or one real solution. 2t^24t=0 
Algebra
in x^2+14=0, how many solutions do we have? 
algebra
For the following equation, state the value of the discriminant and then the nature of the soluation: 3x^28x11=0 Is there one real solution, two imaginary solutions or two real solutions? 
Math
For the following equation, state the value of the discriminant and then describe the nature of the solutions. 9x^2+6x2=0 what is the value of the discriminant? 
Algebra
How many real number solutions does the equation have? 
ALGEBRA CHECK ANSWERS
Solve each equation by graphing the related function. If the equation has no realnumber solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution *** 3x^2=0 … 
Algebra
1. How many real solutions does the function shown on the graph have?