Q1. Graph the function f(x) = (x + 1)^2 - 2 by starting with the basic function and using transformations.

Background

Topic: Transformations of Quadratic Functions

This question tests your understanding of how to graph quadratic functions by applying horizontal and vertical shifts to the basic parabola y = x^2.

Key Terms and Formulas

• Quadratic function:

• Transformation: Shifting, stretching, compressing, and reflecting graphs

• General form: where h shifts horizontally and k shifts vertically

Step-by-Step Guidance

1. Start with the basic graph of , which is a parabola opening upwards with its vertex at (0, 0).

2. Apply the horizontal shift: The term means the graph is shifted 1 unit to the left. So, the new vertex will be at (-1, 0).

3. Apply the vertical shift: The term means the graph is shifted 2 units downward. So, the new vertex will now be at (-1, -2).

4. Sketch the transformed parabola, making sure the shape remains the same (opens upward), but the vertex is at the new location.

Try solving on your own before revealing the answer!