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Answer Key 4.1
Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
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Algebra 2 - Chapter 4.1-4.5
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Using Multiple Strategies to Solve Equations (Lesson 4.1)
Unit 1: sequences and linear functions, day 1: recursive sequences, day 2: applications of arithmetic sequences, day 3: sum of an arithmetic sequence, day 4: applications of geometric sequences, day 5: sequences review, day 6: quiz 1.1 to 1.4, day 7: linear relationships, day 8: point-slope form of a line, day 9: standard form of a linear equation, day 10: quiz 1.5 to 1.7, day 11: unit 1 review, day 12: unit 1 test, unit 2: linear systems, day 1: linear systems, day 2: number of solutions, day 3: elimination, day 4: larger systems of equations, day 5: quiz 2.1 to 2.4, day 6: systems of inequalities, day 7: optimization using systems of inequalities, day 8: quiz 2.5 to 2.6, day 9: unit 2 review, day 10: unit 2 test, unit 3: function families and transformations, day 1: interpreting graphs, day 2: what is a function, day 3: translating functions, day 4: quiz 3.1 to 3.3, day 5: quadratic functions and translations, day 6: square root functions and reflections, day 7: absolute value functions and dilations, day 8: equations of circles, day 9: quiz 3.4 to 3.7, day 10: unit 3 review, day 11: unit 3 test, unit 4: working with functions, day 1: using multiple strategies to solve equations, day 2: solving equations, day 3: solving nonlinear systems, day 4: quiz 4.1 to 4.3, day 5: combining functions, day 6: composition of functions, day 7: inverse relationships, day 8: graphs of inverses, day 9: quiz 4.4 to 4.7, day 10: unit 4 review, day 11: unit 4 test, unit 5: exponential functions and logarithms, day 1: writing exponential functions, day 2: graphs of exponential functions, day 3: applications of exponential functions, day 4: quiz 5.1 to 5.3, day 5: building exponential models, day 6: logarithms, day 7: graphs of logarithmic functions, day 8: quiz 5.4 to 5.6, day 9: unit 5 review, day 10: unit 5 test, unit 6: quadratics, day 1: forms of quadratic equations, day 2: writing equations for quadratic functions, day 3: factoring quadratics, day 4: factoring quadratics. part 2., day 5: solving using the zero product property, day 6: quiz 6.1 to 6.4, day 7: completing the square, day 8: completing the square for circles, day 9: quadratic formula, day 10: complex numbers, day 11: the discriminant and types of solutions, day 12: quiz 6.5 to 6.9, day 13: unit 6 review, day 14: unit 6 test, unit 7: higher degree functions, day 1: what is a polynomial, day 2: forms of polynomial equations, day 3: polynomial function behavior, day 4: repeating zeros, day 5: quiz 7.1 to 7.4, day 6: multiplying and dividing polynomials, day 7: factoring polynomials, day 8: solving polynomials, day 9: quiz 7.5 to 7.7, day 10: unit 7 review, day 11: unit 7 test, unit 8: rational functions, day 1: intro to rational functions, day 2: graphs of rational functions, day 3: key features of graphs of rational functions, day 4: quiz 8.1 to 8.3, day 5: adding and subtracting rational functions, day 6: multiplying and dividing rational functions, day 7: solving rational functions, day 8: quiz 8.4 to 8.6, day 9: unit 8 review, day 10: unit 8 test, unit 9: trigonometry, day 1: right triangle trigonometry, day 2: solving for missing sides using trig ratios, day 3: inverse trig functions for missing angles, day 4: quiz 9.1 to 9.3, day 5: special right triangles, day 6: angles on the coordinate plane, day 7: the unit circle, day 8: quiz 9.4 to 9.6, day 9: radians, day 10: radians and the unit circle, day 11: arc length and area of a sector, day 12: quiz 9.7 to 9.9, day 13: unit 9 review, day 14: unit 9 test, learning targets.
Use graphs, tables, and algebraic methods to find solutions to an equation or to approximate a solution to an equation.
Connect the meaning of a solution across multiple representations.
Activity: Clifford's Cliff Diving
Lesson handouts, media locked.
Our Teaching Philosophy:
Experience first, formalize later (effl), experience first.
This lesson is a high-level task designed to get students thinking about multiple paths to finding a solution and interpreting the meaning of that solution in context and across multiple representations. Encourage students to clearly demonstrate how they are thinking about this problem (using color, diagrams, etc.) and look for students using numerical/tabular, graphical, and analytical representations as you are monitoring. We strongly recommend using Margaret Smith and Mary Kay Stein’s 5 practices approach for facilitating this lesson. Anticipating student approaches is critical to a good consolidation that connects ideas from various groups. As you are talking to groups, express curiosity about students’ thinking and be looking for ways to connect different students’ work during the debrief.
Formalize Later
We understand that students have not formally studied quadratics yet in this course. The goal of this lesson is not for students to use sophisticated algebraic skills (though we hope some students bring some background knowledge from Algebra 1!), but to use a variety of strategies and to connect solutions across multiple representations. Invite at least three groups to share their method for solving this problem, intentionally selecting groups that showcase the three main solution paths. Ask students to summarize each others’ ideas and make connections between representations. For example, ask how we can tell when Cliff hit the water using the table or using the graph. Then ask how information from the equation allowed the group that solved algebraically to find the same value.
If time allows, ask students to discuss the advantages and disadvantages of each representation and when one representation or solution method might be preferable over another.
In the QuickNotes we summarize the three main approaches. In the graphing approach, we simply expect students to notice key points on a graph, such as maxima or intercepts. In future lessons, students will learn more about how solving an equation represents finding an intersection between the curves, but this is not the primary goal of today's lesson.
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The more challenging Algebra 1 problems are quadratic equations of the form ax^2 +bx +c =0, where the general solution is given by the quadratic formula: x = (-b +/- sqrt(b^2-4ac))/2a (where sqrt means a square root of the term in parenthes...
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View Notes - Algebra 2- Chapter 4.1 Homework from MATH Algebra 2 at South Miami Senior High School.
Algebra 2-4.1.4 HW-4-51 to 4-57. 4-51. Gloria is weighing combinations of geometric solids. She found that 4 cylinders and.
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2 . 12 15. 6. Eq. in Vertex Form: Transformations: Vertex: ... What are the transformations on the function 2 . 4 15.
Answer Key 4.1 ; a−2 · 5) ; v−9 · − · ≤ ; 6+x · 12≤
Page 1. 4.1 Circles.notebook. 1. November 04, 2015. Page 2. 4.1 Circles.notebook. 2. November 04, 2015. Page 3. 4.1 Circles.notebook. 3. November 04, 2015
If a < 0, the parabola opens down and the vertex is the highest point of the parabola. minimum value.
Algebra 2 answers, solutions, and theory for high school math, 10th to 11th grade. Like a math tutor, better than a math calculator or problem solver.
Day 2: Applications of Arithmetic Sequences ... Day 4: Quiz 4.1 to 4.3
factor is adding 2. The rule is y = 2x + 7. 4-39. For each equation below