Q1. For the given graph of , answer the following:

• a) Where does ?

• b) Where does ?

• c) Where does ?

Background

Topic: Quadratic Inequalities and Graph Interpretation

This question tests your ability to interpret the graph of a quadratic function and determine where the function is zero, positive, or negative. This is a key skill in college algebra, especially when solving inequalities involving quadratics.

Key Terms and Concepts:

• Zero of a function: The x-values where (the graph crosses the x-axis).

• Positive values: The intervals where the graph is above the x-axis ().

• Negative values: The intervals where the graph is below the x-axis ().

• Quadratic function: A function of the form whose graph is a parabola.

Step-by-Step Guidance

1. Examine the graph and identify the points where the curve crosses the x-axis. These are the solutions to (the zeros or roots of the function).

2. Look for the intervals where the graph is above the x-axis. In these intervals, . For , include both the intervals above the x-axis and the points where the graph touches or crosses the x-axis.

3. Identify the intervals where the graph is below the x-axis. In these intervals, .

4. Write your answers using interval notation, based on the x-values you observe from the graph for each part (a, b, c).

Try solving on your own before revealing the answer!