Q1. Each graph represents a quadratic function. Write each function in factored form.

Background

Topic: Quadratic Functions and Factoring

This question tests your ability to interpret the graph of a quadratic function and express it in factored form. Factored form reveals the roots (x-intercepts) of the function, which are important for solving equations and understanding the behavior of the graph.

Key Terms and Formulas

• Quadratic Function:

• Factored Form: , where and are the roots (x-intercepts)

• Roots: Values of where

Step-by-Step Guidance

1. Examine the graph to identify the x-intercepts (where the curve crosses the x-axis). These are the roots of the quadratic function.

2. Write the function in the form , where and are the x-intercepts you found.

3. Determine the direction of the parabola (upward or downward). If the parabola opens upward, ; if downward, .

4. Use the graph to estimate the value of if possible (for example, check the y-intercept or another point).

5. Set up the factored form using the roots and the value of . Stop here and try to write the function yourself based on the graph.

Try solving on your own before revealing the answer!