To determine the interval where the function $f(x)$ is increasing, we analyze the graph:

1. A function is increasing when its graph goes upward as we move from left to right.
2. From the graph, the function decreases until the vertex (lowest point) and increases after the vertex.

Step-by-Step Solution:

• The vertex of this parabola is at $x = 1$, which is the minimum point.
• The function starts increasing to the right of $x = 1$.
• Therefore, the interval where the function is increasing is: $(1, \infty)$

Final Answer:

• $A = 1$
• $B = \infty$

Let me know if you need more details or further clarification.

Related Questions:

1. How do you determine when a function is decreasing?
2. What is the vertex form of a quadratic function?
3. How can you find the minimum or maximum point of a parabola algebraically?
4. What is the difference between increasing and decreasing intervals?
5. How do derivatives relate to increasing or decreasing behavior of a function?

Tip:

For parabolas in the form $y = ax^2 + bx + c$, the graph increases when $x$ is greater than the vertex $x = -\frac{b}{2a}$ if $a > 0$.