Unit 5 Quadratic Functions and Transformations
Model patterns with functions.
Compare and contrast linear and quadratic functions.
In this lesson, we modeled a quadratic and a linear function and compared representations. We combined a linear function and a quadratic function to examine the representations of the combined function. We noticed that when two functions are added, their corresponding outputs are added to make the new function.
Model a story context with a table, graph, and equation.
Identify features of a function from a graph.
In this lesson, we examined a quadratic function that was a model for area but had many features that were different than those we have seen previously. We learned that all quadratic functions have a linear rate of change and constant second difference, but some may be continuous and have intervals of increase and decrease depending on the domain.
Use patterns to efficiently graph quadratic functions from factored form.
In this lesson, we reviewed how to graph quadratic functions in factored form and standard form. We learned to find the
Find patterns in the equations and graphs of quadratic functions.
In this lesson, we explored transformations of the function
Write equations for functions that are transformations of
Find efficient methods for graphing transformations of
In this lesson, we learned to graph quadratic functions that have a combination of transformations. We found that the vertex form of the equation of a quadratic function makes it easy to find the vertex and identify the transformations. We wrote equations in vertex form from graphs and tables, using our understanding of transformations and the features of parabolas.
Find the square of a binomial expression.
Recognize a perfect square trinomial.
Create perfect squares from partial areas.
Find relationships between terms in a perfect square trinomial.
In this lesson, we connected area models for multiplication to show how to multiply binomials to get a perfect square trinomial. We learned to recognize a perfect square trinomial by looking for a relationship between the second and third terms. We also worked to create a perfect square when given the first two terms of a trinomial.
Find a process for completing the square that works on all quadratic functions.
Adapt diagrams to become more efficient in completing the square.
In this lesson, we solidified a process for completing the square with expressions in the form
Use completing the square to change the form of a quadratic equation.
Graph quadratic equations given in standard form.
In this lesson, we learned to graph a quadratic function in standard form. We used the process of completing the square to help identify the transformations and locate the vertex. From there, we were able to use the quick-graph method to graph the parabola.
Choose the most efficient form of a quadratic function.
Become efficient and accurate in converting from one quadratic form to another.
Become efficient and accurate in identifying features of the graph of quadratic functions from a given form.
In this lesson, we learned to make strategic choices about the most efficient form for working with the graph of a quadratic function. We considered which form is most efficient for obtaining features like the vertex,