![]() ![]() This is something that should be addressed in later lessons. For example, F-IF.B.4 requires that students also be able to interpret key features of functions in terms of their context, but this lesson addresses only the key features of the functions without context. It is not intended for the students to meet the full expectations of the course-level standards addressed through only this lesson. It's important to note that this sample lesson is intended to span multiple class periods, and is the second lesson in an eight-lesson unit on "Quadratics for Career and College Readiness." All other lessons in this unit can be viewed here. Uses explanations and representations to make the mathematics of the lesson explicit.Encourages students to share their developing thinking.Provides entry points for student discussion through suggested dialogue for teachers.Allows for whole group, partner, and individual work in one lesson.Offers an engaging activity that connects students' procedural skill and conceptual understanding of the key features of a quadratic function.Requires students' use of precise course-appropriate mathematical language ( MP.6).Requires students to analyze and see the connection between quadratic functions represented graphically and algebraically.Develops students' understanding of zeros and other key features from the factored form of a quadratic function ( F-IF.B.4).Promotes coherence by highlighting prior knowledge and pointing to the mathematics that will be built from these ideas.Addresses standards F-IF.B.4 and F-IF.C.7.In these cases it is usually better to solve by completing the square or using the quadratic formula. However, not all quadratic equations can be factored evenly. (1,180) (2,90) (3,60) (4,45) (5,36) (6,30) ģ.2: p = -180, a negative number, therefore one factor will be positive and the other negative.ģ.3: b = 24, a positive number, therefore the larger factor will be positive and the smaller will be negative.įactoring quadratics is generally the easier method for solving quadratic equations. Is negative then one factor will be positive and the other negative. This equation is already in the proper form where a = 15, b = 24 and c = -12. Step 1: Write the equation in the general form ax 2 + bx + c = 0. This equation is already in the proper form where a = 4, b = -19 and c = 12.ģ.2: p = 48, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = -19, a negative number, therefore both factors will be negative. Step 8: Set each factor to zero and solve for x. Now that the equation has been factored, solve for x. Using the reverse of the distributive property we can write the outside expressions (shown in red in Step 6) as a second polynomial factor. If this does not occur, regroup the terms and try again. Notice that the parenthetical expression is the same for both groups. ![]() Step 7: Rewrite the equation as two polynomial factors. Step 6: Factor the greatest common denominator from each group. Step 4: Rewrite bx as a sum of two x -terms using the factor pair found in Step 3. If p is negative and b is positive, the larger factor will be positive and the smaller will be negative.ģ.2: p = 12, a positive number, therefore both factors will be positive or both factors will be negative.ģ.3: b = 7, a positive number, therefore both factors will be positive. If p is positive and b is negative, both factors will be negative. If both p and b are negative, the larger factor will be negative and the smaller will be positive. If both p and b are positive, both factors will be positive. If p is negative then one factor will be positive and the other negative.ģ.3: Determine the factor pair that will add to give b. If p is positive then both factors will be positive or both factors will be negative. Step 3: Determine the factor pairs of p that will add to b.įirst ask yourself what are the factors pairs of p, ignoring the negative sign for now. c and find the factors of the result, let's call this p.This equation is already in the proper form where a = 3, b = 7 and c = 4. Step 1: Write the equation in the general form ![]()
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