The range of the function y = x^2 + 4x + 7 is y >= 3
The equation of the function is given as
y = x^2 + 4x + 7
Start by differentiating the above function
So, we have
y' = 2x + 4
Set the above equation to 0
So, we have
2x + 4 = 0
Divide through the equation by 2
So, we have
x + 2 = 0
Evaluate the like terms:
x = -2
Substitute x = -2 in y = x^2 + 4x + 7
y = (-2)^2 + 4(-2) + 7
Evaluate the expression
y = 3
The leading coefficient of the equation y = x^2 + 4x + 7 is positive
This means that the vertex is a minimum
So, the range is
y >= 3
Hence, the range of the function y = x^2 + 4x + 7 is y >= 3
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