Warm Up Do Objective 1b, Page 14 in the End of Course Warm Up Booklet

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Presentation transcript:

Warm Up Do Objective 1b, Page 14 in the End of Course Warm Up Booklet Factor into binomials ( )( ) Do Objective 1b, Page 14 in the End of Course Warm Up Booklet

Warm Up 1.) a2 + 9a + 20 2.) x2 - 9x + 18 3.) a2 - 2a - 15 Factor into binomials ( )( ) 1.) a2 + 9a + 20 2.) x2 - 9x + 18 3.) a2 - 2a - 15 4.) x2 - 17x - 18 5.) 2a2 + 18a + 40

Warm Up 1.) a2 + 9a + 20 (a + 4)(a + 5) 2.) x2 - 9x + 18 (x - 3)(x - 6)

Warm Up 3.) a2 - 2a - 15 (a + 3)(a - 5) 4.) x2 - 17x - 18 (x + 1)(x - 18)

Warm Up 5.) 2a2 + 18a + 40 2(a2 + 9a + 20) 2(a + 4)(a + 5)

Can you think of 2 #’s that you can put in the boxes that solve the following equation without using 0. = .

Zero-Product Property If xy = 0, then what must x and y or both equal? x or y must be 0.

Zero-Product Property If the product of two values is zero, then one or both of the values must be zero.

Zero-Product Property If x(x + 1) = 0, then what do x and (x + 1) or both equal? Then let x = 0 and x + 1 =0 So.. x = 0 or x +1 -1 = 0 -1 x = -1

Zero-Product Property If (2a - 1)(a + 3) = 0, then Let 2a - 1 = 0 & a + 3 = 0 S0… 2a - 1 = 0 a + 3 = 0 2a = 1 a = -3 a = 1/2

Zero-Product Property To solve a quadratic equation, simply set both binomials equal to 0…. Your Turn Solve (x + 3)(x+ 4) = 0

Zero-Product Property Solve (x + 3)(x+ 4) = 0 x + 3 = 0 & x + 4 = 0 x = -3 x = -4

(Solve) 1.) x2 + 6x - 7 = 0 In order to solve a quadratic equation: 1.) First factor 2.) Then set each ( ) = 0

Set both (x - 1) and (x + 7) equal to ZERO. (Solve) 1.) x2 + 6x - 7 = 0 (x- 1)(x +7) = 0 Set both (x - 1) and (x + 7) equal to ZERO. x - 1 = 0 & x + 7 = 0 x = 1 & x = -7

(1)2 + 6(1) - 7 = 0 1 + 6 - 7 = 0 0 = 0 Check 1.) x2 + 6x - 7 = 0 x = 1 and x = -7 (1)2 + 6(1) - 7 = 0 1 + 6 - 7 = 0 0 = 0 True

(-7)2 + 6(-7) - 7 = 0 49 - 42 - 7 = 0 0 = 0 Check 1.) x2 + 6x - 7 = 0 x = 1 and x = -7 (-7)2 + 6(-7) - 7 = 0 49 - 42 - 7 = 0 0 = 0 True

Set both (x ) and (x - 3) equal to ZERO. (Solve) 2.) x2 - 3x = 0 x(x - 3) = 0 Set both (x ) and (x - 3) equal to ZERO. x = 0 & x - 3 = 0 & x = 3

Solving Quadratics What are the 2 steps required to solve a quadratic equation…… 1.) Factor 2.) Solve

Set both (x + 1) and (x + 5) equal to ZERO. Practice (Solve) Your Turn 3.) x2 + 6x + 5 = 0 (x + 1)(x + 5) = 0 Set both (x + 1) and (x + 5) equal to ZERO. x + 1 = 0 & x + 5 = 0 x = -1 & x = -5

. (Solve ) 1.) x2 + 4x - 5 = 0 2.) x2 + x - 6 = 0 3.) x2 - 2x - 3 = 0 4.) x2 - 3x - 10 = 0

Try These (Solve) 1.) x2 + 6x - 7 = 0 2.) x2 + x - 12 = 0 3.) x2 + 6x + 5 = 0 4.) x2 - 4x - 12 = 0