Do Now: Draw the picture. THINK what do you want to find? Ch. 4.4 Factor Quadratic Equation How can I find common binomial factors of quadratic expression with lead coefficient of 1 Do Now: Draw the picture. THINK what do you want to find? On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of the bridge is in the shape of the parabola f(x) = 0.1x2  7x + 250, where f(x) is the height in feet of the cable above the roadway at the distance x feet from a support tower. a. What is the closest the cable comes to the roadway? b. How far from the support tower does this occur? Success Criteria: Today’s Agenda Factor ax2 + bx + c when a is ±1 Find common Factors Do Now Investigate: Factoring Quadratics Assignment

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What do you know? (x - 4)(x +5) FOIL Combine like terms Constant Distribute Coefficient Multiply variables Factors Binomials Product Quadratic Variable Parabola Trinomial Write the problem on a public record and write words that relate to the problem.

Coefficient of Middle Term Let’s Investigate How can I find common binomial factors of quadratic expression with lead coefficient of 1 A. BEFORE Multiplying the binomials, CIRCLE the constant term in the parentheses. These will be constant 1 and constant 2 in the table. 1) (x + 2)(x + 4) = 2) (x + 5)(x + 6) = 3) (x - 1)(x + 6) = 4) (x + 1)(x + 3) = 5) (x + 4)(x - 2) = 6) (x - 3)(x - 3) = B. Fill in the first 2 columns of the table with the numbers you circled. Number Binomial factors Constant 1 Constant 2 Coefficient of Middle Term Constant 3 Simplified Product (trinomial) #1 (x + 2)(x + 4)   #2 (x + 5)(x + 6) #3 (x - 1)(x + 6) #4 (x + 1)(x + 3) #5 (x + 4)(x - 2) #6 (x - 3)(x - 3)

Coefficient of Middle Term Let’s Investigate C. Find the product of each of the expressions from part A. Foil Distribute Simplify 1) (x + 2)(x + 4) = 2) (x + 5)(x + 6) = 3) (x - 1)(x + 6) = 4) (x + 1)(x + 3) = 5) (x + 4)(x - 2) = 6) (x - 3)(x - 3) = Using the product in part C, UNDERLINE the coefficient of the middle term and box the constant term, which will be constant 3 in the table. Complete the table using the information from part C. Number Binomial Factors Constant 1 Constant 2 Coefficient of Middle Term Constant 3 Simplified Product (trinomial) #1 (x + 2)(x + 4) 2   4 6  8   x2 + 6x + 8 #2 (x + 5)(x + 6)  5  6  11  30 x2 + 11x + 30 #3 (x - 1)(x + 6)  -1  -6  x2 + 5x - 6 #4 (x + 1)(x + 3)  1  3  x2 + 4x + 3 #5 (x + 4)(x - 2)  -2  2  -8 x2 + 2x – 8 #6 (x - 3)(x - 3)  -3  9 x2 - 6x + 9

Do Now: Draw the picture. THINK what do you want to find? Ch. 4.4 Factor Quadratic Equation How can I find common binomial factors of quadratic expression with lead coefficient of 1 Do Now: Draw the picture. THINK what do you want to find? Fireworks are fired from the roof of a 100-foot building and travel 84 feet per second. The equation h(t) = -16t2 + 84t + 100 models the height h of the fireworks at any given time t seconds. How long are the fireworks in the air? How high were the fireworks after 2 seconds? Success Criteria: Today’s Agenda Factor ax2 + bx + c when a is ±1 Find common Factors Do Now Investigate: Factoring Quadratics Assignment

Generalize Use the information from the table to answer the questions: (Be ready to Discuss and Share) What do you notice about the coefficient of the linear term in relation to constant 1 and constant 2? What do you notice about the signs? What do you notice about the constant 3 in relation to constant 1 and constant 2? What do you notice about the signs? Using the information, how can we undo distributing? How can we factor a trinomial to 2 binomials? On the Back of your paper lets factor: x2 + 10x2 – 24

Factoring Trinomials x + bx + c Positive b and c 2 Factoring Trinomials x + bx + c Positive b and c Ex 1. x2 + 10x + 24 ( )( ) Trinomials can factor into 2 binomials. When the lead coefficient is 1, the first terms are the square root of the variable. x x + + 1. The signs are determined by term c. If c is positive the signs are the same. 2. Then look at the sign of the b term, if it is (-) they are both (-). If it is (+) then both signs are (+).

Factoring Trinomials x + bx + c Positive b and c 2 Factoring Trinomials x + bx + c Positive b and c Ex 1. x2 + 10x + 24 ( )( ) 3. Determine the factors of c. 24 1 24 2 12 3 8 4 6 x x + + 6 4 4. Because the signs are the same we add the factors together to find the middle value. These are the factors of the trinomial

Factoring Trinomials x - bx + c negative b and positive c 2 Factoring Trinomials x - bx + c negative b and positive c Ex 2. x2 - 13x + 22 ( )( ) 1. Look at sign for c. (positive means same sign) x x - - 2 11 2. Look at the sign for b (-). Then they are both (-). 3. Factor c 22 1 22 2 11 4. What factors are the sum of b?

Factoring Trinomials x2 - bx - c with negative c Ex 3 x2 - 8x – 20 ( )( ) 1. Look at sign for c. (negative means opposite signs) x x + - 2 10 2. Find the factors of c. 20 1 20 2 10 4 5 3. Since signs are opposite you must subtract factors to find the middle term. Keep the signs with the terms.

Practice HW #27 A. x2 - 5x + 4 F. x2 - 5x - 36 B. x2 + 15x + 36 C. x2 - 18x + 45 D. x2 - 7x + 12 E. x2 - 5x - 14 F. x2 - 5x - 36 G. x2 + 18x - 40 x2 + 10x – 24 x2 + 10x + 24 J. x2 + 9x – 13