Quadratic Functions Practice

Practice with Factoring

Objectives

Students will demonstrate their understanding of quadratic functions by identifying characteristics and factoring.

Instructions

For the following questions, students are required to create quadratic functions based on specific characteristics provided.

Question 1

• Task: Make at least two quadratic functions with the following characteristic.
• Characteristic: The functions must have x-intercepts at specified points.

Characteristics to consider:

1. Example of x-intercepts:
   • The quadratic function can be represented in intercept form as: $f(x) = a(x - r_1)(x - r_2)$ Where:
     • $r_1$ and $r_2$ are the x-intercepts and
     • $a$ is a non-zero constant that affects the direction and width of the parabola.

Question 2

• Task: Create another quadratic function with a different set of characteristics.
• Characteristic: The functions must also have x-intercepts but at different points than mentioned in Question 1.

Characteristics to consider:

2. Example of x-intercepts:
   • Similarly, using the intercept form:
     $f(x) = a(x - r_1)(x - r_2)$
   • Ensure that the x-intercepts chosen here differ from those in Question 1.

Conclusion

• By creating quadratic functions with specific x-intercepts, students will gain a better understanding of how the behavior and graph of a quadratic function is affected by its roots and leading coefficient.