Unit 2 Structures of Quadratic Expressions
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.
Multiply two binomials using diagrams.
Factor a trinomial using diagrams.
In this lesson, we used area model diagrams to multiply binomials and factor trinomials. We identified a relationship between the numbers in the factors and the numbers in the equivalent trinomial that helps us to find the factors more easily.
Find patterns in signs and numbers to help factor and multiply expressions.
Use area model diagrams to multiply binomials with different signs.
Use area model diagrams to factor trinomials when some of the terms are negative.
In this lesson, we learned to multiply binomials that had both positive and negative numbers in the factors. We found a useful pattern called “difference of squares” that occurs when the two factors have the same numbers but opposite signs. We learned to factor trinomials that have both positive and negative terms using sign and number patterns to be sure that the factored expression is equivalent to the trinomial.
Use diagrams to factor trinomial expressions when the leading coefficient is not
In this lesson, we learned to factor trinomials in the form
Find patterns to efficiently graph quadratic functions from factored form.
In this lesson, we learned to use the factored form of a quadratic equation to graph parabolas. We learned to find the
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,