A quadratic function $f$ is given below. (a) Determine whether the given quadratic function has a maximum value or a minimum value. Then find this value. (b) Find the range of $f$. \[ f(x)=3 x^{2}-24 x+56 \] (a) Does the quadratic function $f$ have a minimum value or a maximum value? The function $f$ has a minimum value. The function $f$ has a maximum value. What is the minimum or maximum value? $\square$ (Simplify your answer.) (b) What is the range of $f$ ? $\square$ (Type your answer in interval notation.) Time Remaining: 00:50:17 Next

Step 1 ：The given function is a quadratic function in the form of \(f(x) = ax^2 + bx + c\). The coefficient of \(x^2\) is positive, so the parabola opens upwards. This means the function has a minimum value.

Step 2 ：To find the minimum value, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by \(-\frac{b}{2a}\). Substituting \(a = 3\) and \(b = -24\) into this formula, we can find the x-coordinate of the vertex.

Step 3 ：Then, we substitute this x-coordinate into the function to find the y-coordinate, which is the minimum value of the function.

Step 4 ：The range of a function is the set of all possible output values (y-values). Since the parabola opens upwards and has a minimum value, the range of the function is from the minimum value to positive infinity.

Step 5 ：Let's calculate these values. The x-coordinate of the vertex is 4.0. Substituting this into the function, we get the minimum value of the function is 8.

Step 6 ：Final Answer: The function \(f\) has a minimum value of \(\boxed{8}\). The range of \(f\) is \(\boxed{[8, \infty)}\).