Question Use graphing technology to find the range of the function f(x)=-(x-5)^2+4 Answer Attemptiout of 2 square

## Step 1: Identify the Vertex of the Parabola<br />### The function \( f(x) = -(x-5)^2 + 4 \) is a quadratic function in vertex form, \( f(x) = a(x-h)^2 + k \), where \( (h, k) \) is the vertex. Here, \( h = 5 \) and \( k = 4 \). Therefore, the vertex of the parabola is at the point \( (5, 4) \).<br /><br />## Step 2: Determine the Direction of the Parabola<br />### The coefficient \( a = -1 \) indicates that the parabola opens downwards. This means the vertex represents the maximum point on the graph.<br /><br />## Step 3: Find the Range of the Function<br />### Since the parabola opens downwards and the maximum value of the function occurs at the vertex, the range of the function is all values less than or equal to the y-coordinate of the vertex. Thus, the range is \( (-\infty, 4] \).