2. f(x)=x^2-4 x-5 Identify the following information: Vertex & Axis of Symmetry & Increasing Interval & Decreasing Interval & End Behavior &

To analyze the quadratic function \( f(x) = x^2 - 4x - 5 \), we can identify the following characteristics:1. **Vertex**: The vertex of a quadratic function in the form \( f(x) = ax^2 + bx + c \) can be found using the formula for the x-coordinate of the vertex, . Here, , , and . Substitute back into the function to find the y-coordinate: Therefore, the vertex is at \( (2, -9) \).2. **Axis of Symmetry**: The axis of symmetry for a quadratic function is the vertical line that passes through the vertex. Thus, it is given by the equation .3. **Increasing Interval**: A quadratic function \( f(x) = ax^2 + bx + c \) with decreases to the left of the vertex and increases to the right. Since the vertex is at , the function is increasing on the interval \( (2, \infty) \).4. **Decreasing Interval**: Similarly, the function is decreasing on the interval \( (-\infty, 2) \).5. **End Behavior**: For a quadratic function \( f(x) = ax^2 + bx + c \), as , the behavior depends on the sign of . Here, , so: - As , \( f(x) \to \infty \). - As , \( f(x) \to \infty \).In summary: