Q7. Use the graph of the given quadratic function to determine the sign of the leading coefficient a, the vertex, the axis of symmetry, the x-intercepts, the y-intercept, the intervals of increasing/decreasing, and the domain and range.

Background

Topic: Quadratic Functions and Their Graphs

This question tests your ability to interpret the graph of a quadratic function (a parabola) and extract key features such as the vertex, axis of symmetry, intercepts, intervals of increase/decrease, and domain/range.

Key Terms and Concepts:

• Vertex: The turning point of the parabola (either maximum or minimum).

• Axis of Symmetry: The vertical line that passes through the vertex and divides the parabola into two symmetric parts.

• x-intercepts: Points where the graph crosses the x-axis.

• y-intercept: Point where the graph crosses the y-axis.

• Intervals of Increasing/Decreasing: Where the function values are rising or falling as x increases.

• Domain: All possible x-values for the function.

• Range: All possible y-values for the function.

• Leading Coefficient (a): The coefficient of in the quadratic equation .

Step-by-Step Guidance

1. Observe the direction the parabola opens. If it opens upwards, the leading coefficient is positive; if it opens downwards, is negative.

2. Identify the vertex by finding the lowest or highest point on the graph. The vertex has coordinates .

3. Determine the axis of symmetry. This is the vertical line , where is the x-coordinate of the vertex.

4. Find the x-intercepts (if any) by locating where the graph crosses the x-axis. These are points where .

5. Find the y-intercept by locating where the graph crosses the y-axis (where ).

Try solving on your own before revealing the answer!