Unit 2 Day 2 Factoring and Solving.

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Presentation transcript:

Unit 2 Day 2 Factoring and Solving

Warm Up Factor the following x2 + 13x + 40 (x + 8)(x + 5) x2 + 8x + 12

Homework Answers Packet p. 1 #1-9, 19, 20 1. (x – 9)(x + 2) 2. (p – 7)(p + 2) 3. (m – 8)(m – 1) 4. (x – 9)(x – 7) 5. (x + 7)(x + 4) 6. (k + 8)(k – 3) (x – 9)(x – 4) 8. (b + 7)(b – 3) (p – 6)(p + 2) 19. 7, 8, 13, -7, -8, -13 20. c

Homework Answers Finish Notes p. 5 1. (x + 2)2 2. (x + 3)(x + 2) 3. (x - 3)2 4. (x – 4)(x – 3) 5. (x - 5)(x - 6) 6. (x + 3)(x - 2) (x + 6)(x – 3) 8. (x – 5)(x + 3) (x + 3)(x - 3) 10. (x – 4)(x + 4)

Notes p. 6: Review from CCM1: Graph the equation y = x2 + 13x + 40 on your calculator. Use your calculator to find the zeroes: x = ___ and x = ___ From the warm-up, the factors of y = x2 + 13x + 40 are . Set each factor equal to zero and solve for x. x + 5 = 0 x + 8 = 0 x = x = What do you notice about your answers and the zeroes you found earlier on your calculator?

Summary: To solve a quadratic with your calculator Enter the equation into “y =” and use the “zero” function. (You did this in CCM1)

To solve a quadratic algebraically (this is new) Set the equation equal to zero Factor the equation Set each factor equal to zero and solve Example: Solve x2 + 8x = -12

Practice Solve each quadratic algebraically. Check your answers using the zero function on your calculator. 11) x2 + 4x = -4 12) x2 + 5x = -6 13) x2 + 9 = 6x 14) x2 + 12 = 7x x = -2 x = -3, -2 (double root) x = 3 x = 3, 4

Day 2: Factoring when a ≠ 1 (Busting the “B”) What if the problem has “a” value that is not equal to 1? For example, 4x2 + 8x + 3 = 0: How can we algebraically find where this graph = 0? The concept of un-distributing is still the same!! 4x2 + 8x + 3 = 0 In this case we need to find out what multiplies to give us a • c but adds to give us b. Let’s list all the factors of 4 • 3 or 12: 1 • ____ 2 • ____ 3 • ____ 12 6 4

Which one of those sets of factors of 12 also add to give us the b value, 8? Rewrite the original equation using an equivalent structure: 1 • ____ 2 • ____ 3 • ____ 12 6 4 Remember!! It doesn’t matter which order you write the factors in! Group the first two and last two! Undistribute what is common to both terms Create factors out of the repeated factor, and the undistributed factors Use multiplication (box, distribution, or FOIL) to check that it is equal to what you started with!

Practice Solve. 1) 2x2 + 5x + 3 = 0 2) 2x2 + 9x + 10 = 0 3) 3x2 + 18x + 15 = 0 4) 3x2 + 13x = 10 x = -1, -3/2 x = -5/2, -2 x = -1, -5 x = 2/3, -5 Give about 5-10 minutes to practice OR Skip if low on time….to make room for factoring game.

Factoring Around the Room!! Review! Factoring Around the Room!! Factoring Review Game Question Work Solution(s) Word Select a color to work on. Only work on that color. Key: Green: Basic Yellow: Medium Blue: Advanced This will be turned in…

Homework Packet Pg 2