Warm-up: Create two binomials then multiply them to create their product. Describe the key features of the product of two binomials? Varies... Collect Test Mod 5 Corrections Collect Week 5 Warmups

Homework Check:

M1 7.8 Nothing Could Be Finer Objectives: Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function. Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities. Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; and maximums and minimums.

Define: Algebra Tiles? Graph Paper? Use manipulatives to explain.

Monitor group work #1 and #2 for students practicing their work around key features of quadratic functions and how they relate to the context the function describes. What are the feasible x-intercepts? What does it mean when the function is below the x-axis? What does the y-intercept mean in the context of the problem? How can you tell when the profit is increasing fastest? How do you find the price for a corresponding profit? Where is the maximum profit located? Where is the maximum profit located in terms of the x-intercepts? What does the vertex tell you in terms of increasing/decreasing behavior?

$6 Anything more than $2. The Nest would break even if they sold the hat for $2 since that is the smallest x-intercept. P(0) = (0, -192.5). This means it cost The Nest $19,250 to print the hats.

Students will estimate for the graph. Sample answer: $4.50 or $7.50. Domain: 2 < x < 10 or (2, 10) Range: 0 < y < 154 or (0, 154]

(2, 3) because the y values increased the most (0 to 80). Any price greater than 6 will decrease the profit and people probably don’t want to spend more than that for a State Fair hat.

d. A & D have the same coefficient but have opposite signs. Sample answers: a. The ones opening down (D & E) must have a negative coefficient in front of the factors. b. The ones opening up (A, B, & C) must have a positive coefficient in front of the factors. c. The value of the coefficients in E & C must be larger than the coefficients in A, B, & D because E & C are narrower than A, B, & D. d. A & D have the same coefficient but have opposite signs. e. E & C have the same coefficient but have opposite signs. Have students work on # 3 and 4. How are the factors related to the graph of the parabola? Can you find the y-intercept by using the function instead of the graph? How can you tell of the graph is going to open up or down? Why are some of the parabolas wider than others?

P(x) = a(x - 2)(x - 10). Students should plug in a point to find a.

Discuss: The leading coefficient determines how narrow or wide the graph of the parabola is. The zeros of the factors are the zeros of the x-intercepts. The y-intercept can be found by evaluating f(0).

Exit ticket for students: 4 3 6 2 Check graphs left to right. 1 5

Classwork: p. 34 R HOMEWORK: p. 47-50 SG