Transforming Parabolas Investigation
This 1-page investigation guides 9th graders in exploring the effects of parameters a, h, and k on the graph of a quadratic function in vertex form, y=a(x-h)^2 + k. Students will use a graphing tool to understand translations, stretches, compressions, and reflections, while also identifying key points related to the parameters.
“TRANSFORMING PARABOLAS Use your graphing tool or Transforming Parabolas (Desmos) to investigate the impact of the parameters, a, h, and k, in the graphing form of a quadratic function, y=a(x-h)^2 +k : Which parameter translates the graph of horizontally (right or left)? What values of the parameter translate to the left? To the right? Which parameter stretches or compresses the graph of vertically? What values of the parameter stretch the graph? What values compress the graph? What values of which parameter will reflect the graph of across the x-axis? Which parameter translates the graph of vertically (up or down)? What values of the parameter translate up? Down? Why? Are there any points on the graph of a parabola that have a connection to specific parameters in the equation? Explain.”
Teacher Guide & Tips
- Use this activity as a 45-minute introduction to transforming parabolas or as a review.
- Discussion question: How does the sign of 'a' affect the parabola's orientation, and what does this tell us about reflections?
- Scaffold for struggling students: Provide a partially completed table of values for specific parameter changes to help them see the patterns.
- Extension for advanced students: Ask students to investigate the effect of changing the parameter 'a' on the vertical stretch/compression and compare it to the effect of changing 'a' on horizontal stretch/compression (if applicable in a different form).
- Estimated time: 45 minutes.
What is Diffit?
Teachers use Diffit to get quality materials for their unique classrooms. Adjust difficulty, add scaffolds, or change the topic to get started.
Try Diffit for free“TRANSFORMING PARABOLAS Use your graphing tool or Transforming Parabolas (Desmos) to investigate the impact of the parameters, a, h, and k, in the graphing form of a quadratic function, y=a(x-h)^2 +k : Which parameter translates the graph of horizontally (right or left)? What values of the parameter translate to the left? To the right? Which parameter stretches or compresses the graph of vertically? What values of the parameter stretch the graph? What values compress the graph? What values of which parameter will reflect the graph of across the x-axis? Which parameter translates the graph of vertically (up or down)? What values of the parameter translate up? Down? Why? Are there any points on the graph of a parabola that have a connection to specific parameters in the equation? Explain.”
Teacher Guide & Tips
- Use this activity as a 45-minute introduction to transforming parabolas or as a review.
- Discussion question: How does the sign of 'a' affect the parabola's orientation, and what does this tell us about reflections?
- Scaffold for struggling students: Provide a partially completed table of values for specific parameter changes to help them see the patterns.
- Extension for advanced students: Ask students to investigate the effect of changing the parameter 'a' on the vertical stretch/compression and compare it to the effect of changing 'a' on horizontal stretch/compression (if applicable in a different form).
- Estimated time: 45 minutes.
Transforming Parabolas Investigation
This 1-page investigation guides 9th graders in exploring the effects of parameters a, h, and k on the graph of a quadratic function in vertex form, y=a(x-h)^2 + k. Students will use a graphing tool to understand translations, stretches, compressions, and reflections, while also identifying key points related to the parameters.
What is Diffit?
Teachers use Diffit to get quality materials for their unique classrooms. Adjust difficulty, add scaffolds, or change the topic to get started.
Try Diffit for free