Ch. 4.4 Factor Quadratic Equation I can find common binomial factors of quadratic expression with lead coefficient of 1 Do Now: On a suspension bridge,

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Ch. 4.4 Factor Quadratic Equation I can find common binomial factors of quadratic expression with lead coefficient of 1 Do Now: On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of one bridge is in the shape of the parabola y = 0.1x2  7x + 150, where y 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 Check HW Lesson Assignment

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

Practice A. x2 + 5x + 6 B. -x2 - 13x - 30 C. x2 + 20x + 75 D. x2 + 7x + 5

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?

Practice A. x2 - 5x + 4 B. x2 - 15x + 36 C. x2 - 18x + 45 D. -x2 + 7x - 12

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 A. -x2 + 5x + 14 B. x2 - 5x - 36 C. x2 + 18x - 40 D. x2 + 18x - 40