To determine the increasing or decreasing nature of a quadratic function at specific points, you can analyze the sign of the derivative of the function at those points. Here's how you can approach the problem step by step:
1. **Find the Quadratic Function**: First, identify the quadratic function that you are working with. In this case, the provided information is not a quadratic function, so we'll need to have the actual function to proceed.
2. **Calculate the Derivative**: Once you have the quadratic function, calculate its derivative. The derivative of a function indicates its slope at any given point. For a quadratic function, this derivative will be a linear function.
3. **Evaluate the Derivative at x = 0, x = 1, and x = -3**: Plug in the values x = 0, x = 1, and x = -3 into the derivative function you calculated in step 2. Evaluate the signs of the resulting values.
4. **Interpret the Results**:
- If the derivative is positive at a specific point, the function is increasing at that point.
- If the derivative is negative at a specific point, the function is decreasing at that point.
By following these steps with the actual quadratic function provided, you can determine whether the function is increasing or decreasing at x = 0, x = 1, and x = -3.
