Q24 & Q25. Find the vertex, x-intercept(s), y-intercept, and axis of symmetry for each quadratic function. Sketch the function.

Background

Topic: Quadratic Functions and Their Graphs

These questions test your understanding of how to analyze and graph quadratic functions, including finding key features such as the vertex, intercepts, and axis of symmetry.

Key Terms and Formulas:

• Vertex: The highest or lowest point of the parabola, given by for .

• x-intercepts: Points where the graph crosses the x-axis, found by solving .

• y-intercept: Point where the graph crosses the y-axis, found by evaluating .

• Axis of symmetry: Vertical line passing through the vertex, .

Step-by-Step Guidance

1. For , identify the form: This is in vertex form , so the vertex is .

2. For , use the formula to find the x-coordinate of the vertex.

3. Plug the x-coordinate back into the function to find the y-coordinate of the vertex.

4. To find x-intercepts, set and solve for (use factoring or the quadratic formula).

5. To find the y-intercept, substitute into the function.

6. Write the axis of symmetry as or .

Try solving on your own before revealing the answer!