To answer the question based on the provided graph:

Observations:

• The graph shows a parabolic curve that opens downward.
• This is a quadratic function, and it appears to have a vertex at $(0, 5)$.
• The function increases from the left side of the graph until it reaches the vertex and then decreases afterward.

Answering part a:

a. Increasing Intervals:

• The function is increasing when moving left to right up to the vertex at $x = 0$.
• This happens on the open interval $(-∞, 0)$.

So, the correct interval for a is: $(-∞, 0)$

Would you like more details, or do you have any other questions?

Related Questions:

1. What is the interval where the function is decreasing?
2. How do we determine if a function is constant from its graph?
3. What would be the effect of shifting the parabola vertically or horizontally?
4. Can this function have any horizontal asymptotes? Why or why not?
5. How can we find the domain and range of this function?

Tip:

When working with quadratic functions, always look at the vertex to find where the function transitions from increasing to decreasing.