Question 4 6 pts Use technology to graph the quadratic function $y=-\frac{1}{10} x^{2}+5 x-12$. Select the domain and range and find the minimum or maximum value. domain: $(2.528,47.472)$ range: $(-\infty, 50.5]$ absolute maximum $=25$ domain: $(-\infty, \infty)$ range: $(50.5, \infty)$ absolute minimum $=50.5$ domain: $(-\infty, \infty)$ range: $(-\infty, \infty)$ absolute maximum $=25$ domain: $(-\infty, \infty)$ range: $(-\infty, 50.5]$ absolute maximum $=50.5$

Step 1 ：The given quadratic function is \(y=-\frac{1}{10} x^{2}+5 x-12\).

Step 2 ：Since the coefficient of \(x^2\) is negative, the parabola opens downwards. This means the vertex of the parabola is the maximum point.

Step 3 ：The domain of a quadratic function is always \((-\infty, \infty)\) because the function is defined for all real numbers.

Step 4 ：The range of a quadratic function that opens downwards is \((-\infty, k]\) where k is the y-coordinate of the vertex.

Step 5 ：The maximum value of the function is the y-coordinate of the vertex.

Step 6 ：The vertex of a parabola \(y=ax^2+bx+c\) is given by the point \((-\frac{b}{2a}, f(-\frac{b}{2a}))\).

Step 7 ：So, we need to find the vertex of the parabola to determine the range and the maximum value.

Step 8 ：The x-coordinate of the vertex is 25 and the y-coordinate of the vertex is 50.5.

Step 9 ：Therefore, the domain of the function is \((-\infty, \infty)\), the range of the function is \((-\infty, 50.5]\), and the maximum value of the function is 50.5.

Step 10 ：Final Answer: The domain of the function is \((-\infty, \infty)\), the range of the function is \((-\infty, 50.5]\), and the maximum value of the function is \(\boxed{50.5}\).