The image shows a question with a graph of a quadratic function $y = f(x)$, likely a parabola opening upwards. Based on this, the question seems to ask the following:

1. Part (a): Determine the interval where the function $f(x)$ is decreasing.
2. Part (b): Determine the interval where the function $f(x)$ is increasing.

Solving the problem:

• Decreasing Interval: A function decreases where the slope of the tangent is negative, typically where the graph slopes downwards as you move from left to right. For a parabola opening upwards, this occurs on the left side of the vertex.
• Increasing Interval: The function increases where the slope of the tangent is positive, i.e., where the graph slopes upwards as you move from left to right, which happens on the right side of the vertex.

Let me first extract the vertex point from the image and the intervals from the graph. Based on the general shape of the graph:

1. If the vertex is at $x = a$, the function $f(x)$ is:
   • Decreasing on the interval $(-\infty, a)$
   • Increasing on the interval $(a, \infty)$

Would you like a detailed explanation or confirmation of the exact vertex and intervals based on the image? Additionally, here are 5 related questions:

1. How do you find the vertex of a quadratic function algebraically?
2. How do you determine whether a function is increasing or decreasing without a graph?
3. What is the significance of the derivative in finding increasing and decreasing intervals?
4. Can a function have more than one interval of increase or decrease?
5. How