Which statement about the function `n\left(x\right)=5x^{2}-20x+12`is true?
The domain of the function is x≥2 The domain of the function is x≥0 The range of the function is n(x)≥-8 The range of the function is n(x)≤12
The statement "The range of the function is n(x)≥-8" is true.
To find the range of the function, we need to determine the minimum value that n(x) can take. This can be done by finding the vertex of the quadratic function.
The vertex of the function n(x)=5x^2-20x+12 can be found using the formula x = -b/2a.
In this case, a=5 and b=-20.
So, x = -(-20)/(2*5) = 20/10 = 2.
Now substitute x=2 in the function to find the minimum value of n(x):
n(2) = 5*(2)^2 - 20*(2) + 12
n(2) = 5*4 - 40 + 12
n(2) = 20 - 40 + 12
n(2) = -8
Therefore, the minimum value of n(x) is -8, which means the range of the function n(x) is n(x)≥-8.