Which of the following could be the graph of 

The correct answer is:

Hint:
Concept used in the question is concept of graph of the quadratic equation.
Quadratic equation has two solutions.
Points at which graph cut x-axis are the solution.
In quadratic equation is D (Discriminant) is given by b² - 4ac.
If D = 0, then equation have equal roots.
D > 0 then, equation has two real roots.
D < 0 then, equation has imaginary roots
Roots of quadratic equation are given by  where D is discriminant.
Step by step explanation:
Given:
Equation: y = x² + 2x + 2
Step 1:
Find Discriminant i. e D
D = b² - 4ac
⇒ D = 2² - 4(1) (2)
⇒ D = 4 - 8
⇒ D = - 4
As the D < 0 therefore equation has no real roots.
∴ y = x² + 2x + 2 will never cut x-axis.
Step 2:
Find the minimum value of y = x² + 2x + 2
Differentiate w.r.t. X

⇒ 2x + 2
Equate 2x + 2 to zero, we will point at which function is maximum or minimum
⇒ 2x + 2 = 0
⇒ 2x = - 2
⇒ x = 
⇒ x = - 1
Step 3:
Determine if at point x = - 1, function is max. or min.
⇒ if y” > o, y is minimum
if y” < o, y is maximum
⇒ y” =  ( 2x + 2)
⇒ y” = 2
∴ y is minimum at point x = - 1.
Hence, we concluded that graph do not cross x-axis and has minimum value at x = - 1.