Collect Quarter 4 Week 4 Warmups What strategies can be used to perform multiplication operations on polynomials? Varies..Ex: Distributive Property Collect Quarter 4 Week 4 Warmups

Homework Check:

6x/2 (22x+3) cm

M1 7.3 State Fair Flyer Objectives: Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions. Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction or two linear functions with multiplication.

With your seat buddy, look over the questions for 7. 3 With your seat buddy, look over the questions for 7.3. How are they similar/different from past experiences in math?

With your partner, answer questions Set timer for 10 minute increments. With your partner, answer questions #1-13. You will switch partners when the timer sounds. We will check this today!

4x - 12 8 2x - 2 Algebra Tiles? Graph Paper? Use manipulatives to explain.

Answers will vary: h(x) = x + 1 Sample Answer: f(x) = 2x - 3, g(x) = -x + 4 Algebra Tiles? Graph Paper? Use manipulatives to explain. No. In the sample answer given, the x-intercept of f(x) is 3/2 and the x-intercept of g(x) is 4. 3/2 + 4 does not equal -1, the x-intercept of h(x).

g(x) = -4x + 7 h(x) = 11 Answers will vary. Sample answer: h(x) is a horizontal line because when we combined the two functions, the x terms summed to zero, leaving us with just a constant term of 11 and a slope of zero. Algebra Tiles? Graph Paper? Use manipulatives to explain.

No. When you combine two linear functions, you always get a function No. When you combine two linear functions, you always get a function. A vertical line is not a function. 2 - 6x Algebra Tiles? Graph Paper? Use manipulatives to explain. 5n + 4

ie. (2x - 5y = 10) + (4x + 3y = 12) produces 6x - 2y = 22 No, not unless you convert them to slope-intercept (y=mx+b) form first, where y is written as a function of x. If you combine them in standard form, you are combining both the x-terms and the y-terms (as well as the constant terms), while maintaining equality of the left and right sides of the equation. ie. (2x - 5y = 10) + (4x + 3y = 12) produces 6x - 2y = 22 When you add two linear functions together, you are combining the x-terms and the constant terms to produce a new function whose y-values are the sum of the y-values of the two functions. For example, for the first and second lines respectively, f(x) = 2/5x - 2, g(x) = -4/3x + 4 give the sum f(x) + g(x) = -14/15x +2, which is not the same as the equation 6x - 2y = 22 written in slope-intercept form y = 3x -11. Algebra Tiles? Graph Paper? Use manipulatives to explain.

f(x) = x + 3; g(x) = 2x - 5; (f - g)(x) = - x + 8 OR The y-intercept of (f - g)(x) is the difference of the y-intercepts of f(x) and g(x). Algebra Tiles? Graph Paper? Use manipulatives to explain. Answers may vary depending on whether they view f(x) as a discrete function. If so, the domain of (f - g)(x) is the same as the domain of f(x) (a subset of the domain of (g(x)). The range of (f - g)(x) is the difference between the y-values of f(x) and g(x) for the x-values of f(x).

Algebra Tiles? Graph Paper? Use manipulatives to explain.

12y + 2 Algebra Tiles? Graph Paper? Use manipulatives to explain.

B Algebra Tiles? Graph Paper? Use manipulatives to explain.

8x + 10y + 12x + 15y = 20x + 25y Yes. The slope of the sum of the two lines would be the sum of the slopes of the two lines because you would be combining the linear terms. Algebra Tiles? Graph Paper? Use manipulatives to explain. Sometimes. When the slopes are zero, they would be parallel. Otherwise, the slope of f(x) + g(x) would be twice the slope of f(x) or g(x). Since f(x) and g(x) are parallel, they have the same slope, so their sum would be twice the slope.

Exit ticket for students:

Classwork: p. 13-16 HOMEWORK: p. 17-20 RSG