U2D0 Quadratics Outline MCR 3UI Printable copy of the Unit 2 Outline
U2 All Worksheets This is a scan of all unit 2 worksheets that you may print if you prefer that over looking at the electronic version.
| Day | Title | Practice Questions |
1 | U2D1_S Radicals NO CALCULATORS FOR THIS LESSON! U2D1_T Radicals MCR 3UI | Pgs. 106-107 #1-4 U2D1 p 106 hw solutions Pgs. 139-141 #1ae, 2ae, 3-odds, 4aceg, 5bfjm, 12, 14 U2D1_p_139-hw-solutions U2D1 Worksheet Radicals Extra Practice MCR3UI U2D1 Worksheet Solutions Radicals Extra Practice NO CALCULATORS! |
| X | Rationalizing Denominator (OPTIONAL) U2D1b_S Rationalizing the Denominator REMOVED FROM this semester | XPage 140 5gikln, 6aefjk, 7bdfhj, 12, 14 |
2 | U2D2_S Functions-vs-relations and Function Notation U2D2_T Functions-vs-relations and Function Notation MCR 3UI khanacademy video-what-is-a-function? | Pgs. 178-181 #1-2, 3acd, 4, 5, 6a, 7a, 8a, 9a, 10a, 12cd, 14, 17, 25, 29 U2D2 Page 179_181 HW Solutions U2D2 Worksheet Function Notation U2D2 Worksheet Solutions Function Notation |
3 | U2D3a_S Properties of Quadratics (three forms) & U2D3-S Partial Factoring U2D3a_T Quadratic Function Properties MCR 3UI | U2D3 Worksheet Quadratic Functions U2D3 Worksheet Solutions Quadratic Functions |
4, 5 | Quiz Radicals – no calculator! U2D4_S Max and Mins U2D4_T Max and Mins MCR 3UI | U2D4 Worksheet Maximums & Minimums U2D4 Worksheet Solutions Maximums & Minimums |
6 | U2D5_S Quadratic Equations U2D5_T Quadratic Equations MCR 3UI | U2D5 Worksheet Quadratic Equations U2D5 Worksheet Solutions Quadratic Equations |
| U2D6_S Real-World Applications | U2D6 Worksheet Real-World Application Problems U2D6 Worksheet Solutions Real-World Application Problems | |
QUIZ (No calculator for radical part) & Work Period | U2_ QUIZ REVIEW U2_ QUIZ REVIEW Solutions Catch up on Homework | |
7 | U2D8_S Solving Inequalities U2D8_T Solving Inequalities MCR 3UI | U2D8 Worksheet Inequalities U2D8 Worksheet Solutions Inequalities |
8 | Quiz – Quadratics including Domain & Range U2D9_S Zeros and the Discriminant U2D9_T Zeros and the Discriminant MCR 3UI | U2D9 Worksheet Zeros & The Discriminant U2D9 Worksheet Solutions Zeros & The Discriminant |
9 | U2D10_S Systems of Equations Involving Quadratics U2D10_T Systems of Equations Involving Quadratics MCR 3UI | U2D10 Worksheet Solving Quadratic Systems U2D10 Worksheet Solutions Solving Quadratic Systems |
10 | U2D11-S Families-of-Quadratics U2D11-T Family-of-Functions | U2D11 Worksheet Family-of-Quadratics U2D11 Worksheet Solutions Family-of-Quadratics |
11 | Review U2D12_S Review Period U2D12_T Review Period March 9th – first lesson Unit 3 | U2D12 Worksheet Quadratics Review U2D12 Worksheet Solutions Quadratics Review NOTE: there are corrections to #8, 18 Question 8(a) should have been the year 2020 Question 18 Range is y less than or equal to 0. Corrections have been made to the question paper above. |
12 | TEST |
Unit 2 Structures of Quadratic Expressions
Lesson 1
Learning Focus
Find patterns in the equations and graphs of quadratic functions.
Lesson Summary
In this lesson, we explored transformations of the function . We found vertical and horizontal shifts, reflections, and vertical stretches of the parabola. We justified why changes to the equation transform the graph, using tables and our understanding of functions.
Lesson 2
Learning Focus
Write equations for functions that are transformations of .
Find efficient methods for graphing transformations of .
Lesson Summary
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.
Lesson 3
Learning Focus
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.
Lesson Summary
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.
Lesson 4
Learning Focus
Find a process for completing the square that works on all quadratic functions.
Adapt diagrams to become more efficient in completing the square.
Lesson Summary
In this lesson, we solidified a process for completing the square with expressions in the form with . We learned an algebraic procedure that goes along with an open diagram that supports our work. We also verified that the expression obtained by completing the square was equivalent to the original expression using the distributive property.
Lesson 5
Learning Focus
Use completing the square to change the form of a quadratic equation.
Graph quadratic equations given in standard form.
Lesson Summary
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.
Lesson 6
Learning Focus
Multiply two binomials using diagrams.
Factor a trinomial using diagrams.
Lesson Summary
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.
Lesson 7
Learning Focus
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.
Lesson Summary
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.
Lesson 8
Learning Focus
Use diagrams to factor trinomial expressions when the leading coefficient is not .
Lesson Summary
In this lesson, we learned to factor trinomials in the form when . Sometimes the terms have a common factor that can be factored out, leaving an expression that is much easier to work with. When there is not a common factor, diagrams can be used to help think about the number and sign combinations that work to make the factored expression equivalent to the trinomial.
Lesson 9
Learning Focus
Find patterns to efficiently graph quadratic functions from factored form.
Lesson Summary
In this lesson, we learned to use the factored form of a quadratic equation to graph parabolas. We learned to find the -intercepts from the factors, then find the line of symmetry between the -intercepts. Once we knew the line of symmetry, we could find the vertex. We observed several patterns that helped to make factored form an efficient way to graph quadratics.
Lesson 10
Learning Focus
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.
Lesson Summary
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, -intercepts, -intercept, the vertical stretch, and reflection. We also considered which form will be most efficient to convert from standard form, knowing that some trinomials do not factor easily and some trinomials make completing the square complicated.