Quadratic Functions and Modeling
This packet guides 9th graders through building and interpreting quadratic expressions and equations to model real-life phenomena. It focuses on constructing and analyzing quadratic functions from data, understanding their graphical characteristics, and comparing their rates of change to linear functions.
“Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. Interpret quadratic expressions and parts of a quadratic expression that represent a quantity in terms of its context. Estimate, calculate, and interpret the average rate of change of a quadratic function and make comparisons to the average rate of change of linear functions. Identify the effect on the graph generated by a quadratic function when replacing f(x) with f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Graph and analyze the key characteristics of quadratic functions. Compare characteristics of two functions, each represented in a different way.”
Teacher Guide & Tips
- Use this packet as a 2-3 day lesson block on quadratic functions.
- Discussion question: How can quadratic functions be used to model projectile motion or optimize area?
- For struggling readers, provide sentence frames for interpreting the meaning of coefficients and constants in real-world contexts.
- Advanced students can explore the effects of transformations on the vertex form of a quadratic function and relate it to the parent function.
- Estimated time: 2-3 class periods.
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Try Diffit for free“Build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations. Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. Interpret quadratic expressions and parts of a quadratic expression that represent a quantity in terms of its context. Estimate, calculate, and interpret the average rate of change of a quadratic function and make comparisons to the average rate of change of linear functions. Identify the effect on the graph generated by a quadratic function when replacing f(x) with f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs. Graph and analyze the key characteristics of quadratic functions. Compare characteristics of two functions, each represented in a different way.”
Teacher Guide & Tips
- Use this packet as a 2-3 day lesson block on quadratic functions.
- Discussion question: How can quadratic functions be used to model projectile motion or optimize area?
- For struggling readers, provide sentence frames for interpreting the meaning of coefficients and constants in real-world contexts.
- Advanced students can explore the effects of transformations on the vertex form of a quadratic function and relate it to the parent function.
- Estimated time: 2-3 class periods.
Quadratic Functions and Modeling
This packet guides 9th graders through building and interpreting quadratic expressions and equations to model real-life phenomena. It focuses on constructing and analyzing quadratic functions from data, understanding their graphical characteristics, and comparing their rates of change to linear functions.
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