Chapter 7

  1. 1. 2x2 + 5x = 122x2 + 5x − 12 = 0(2x − 3)(x + 4) = 02x − 3 = 0x + 4 = 0x = 32orx =  − 4

  2. 2. x2 = 3x + 5x2 − 3x − 5 = 0a = 1 , b =  − 3 , c =  − 5x =  − ( − 3) ± ( − 3)2 − 4(1)( − 5)2(1) = 3 ± 292

  3. 3. 4x2 − 5x − 3 = 0

    On calculator

    Y1 = 4X2 − 5 − 3

    From zero feature

    x =  − 0.44or x = 1.69

    A parabola opens upward, falls through (negative 0.44, 0) to a vertex in quadrant 4, then rises through (1.69, 0).

  4. 4. 2x2 − x = 6 − 2x(3 − x)2x2 − x = 6 − 6x + 2x25x = 6(not quadratic)x = 65

  5. 5. 3x − 2x + 2 = 1LCD = x(x + 2)3x(x + 2)x − 2x(x + 2)x + 2 = x(x + 2)3(x + 2) − 2x = x2 + 2x3x + 6 − 2x = x2 + 2x0 = x2 + x − 6(x + 3)(x − 2) = 0x =  − 3 ,  2

  6. 6. y = 2x2 + 8x + 5 − b2a =  − 82(2) =  − 2y = 2( − 2)2 + 8( − 2) + 5 =  − 3

    Min. pt. (a > 0) is ( − 2 ,  − 3) , 

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