The function y = x^2 + 8x + 12 describes the graph given in the question.
What is a function?
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable).
Let's find out at which points the value of function is zero:
x^2 + 8x + 12 = 0
x^2 + 6x + 2x + 12 = 0 (Mid term splitting)
x(x + 6) + 2(x + 6) = 0
(x + 6)(x + 2) = 0
x = -2 , -6
The zeroes of the function are x = -2 and x = -6 respectively, and it is visible in the graph that the function gives a zero value at (-2,0) and (-6,0).
Hence the correct answer is y = x^2 + 8x + 12, option(D).
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