What is the range of the function f(x)= 3x2-12x+7?
What is the range of the function f(x)= 3x2-12x+7?
y≤-5
y≥-5
y≤-7
y≥-7
The range of the function f(x) = 3x^2 - 12x + 7 can be determined by finding the minimum or maximum value of the function. We can do this by finding the vertex of the parabola defined by the quadratic function.
The vertex of the parabola defined by the function f(x) = ax^2 + bx + c is given by the formula x = -b/2a. In this case, a = 3 and b = -12, so the x-coordinate of the vertex is x = -(-12)/(2*3) = 2.
Substitute x = 2 back into the function to find the y-coordinate of the vertex: f(2) = 3(2)^2 - 12(2) + 7 = 3(4) - 24 + 7 = 12 - 24 + 7 = -5.
Therefore, the minimum value of the function occurs at x = 2 and is equal to -5. This means that the range of the function is y ≥ -5.