<u>vertex</u> y = 3(x - 2)² - 4 y = 3((x - 2)(x - 2)) - 4 y = 3(x² - 2x - 2x + 4) - 4 y = 3(x² - 4x + 4) - 4 y = 3(x²) - 3(4x) + 3(4) - 4 y = 3x² - 12x + 12 - 4 y = 3x² - 12x + 8 3x² - 12x + 8 = 0 x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u> 2(3) x = <u>12 +/- √(144 - 96)</u> 6 x = <u>12 +/- √(48) </u> <u> </u> 6<u> </u>x =<u> 12 +/- 6.93</u> <u /> 6 x = 2 +/- 1.155 x = 2 + 1.155 x = 2 - 1.155 x = 3.155 x = 0.845 y = 3x² - 12x + 8 y = 3(3.155)² - 12(3.155) + 8 y = 3(1.334025) - 3.786 + 8 y = 4.002075 - 3.786 + 8 y = 0.216075 + 8 y = 8.216075 (x, y) = (3.155, 8.216075) or y = 3x² - 12x + 8 y = 3(0.845)² - 12(0.845) + 8 y = 3(0.714025) - 10.14 + 8 y = 2.142075 - 10.14 + 8 y = -7.857925 + 8 y = 0.142675 (x, y) = (0.845, 0.142675) <u>y-intercept</u> y = 3x² - 12x + 8 y = 3(0)² - 12(0) + 8 y = 3(0) - 0 + 8 y = 0 - 0 + 8 y = 0 + 8 0 = -y + 8 y = 8 (x, y) = (0, 8) ------------------------------------------------------------------------------------------- <u>vertex</u> y = 4(x - 5)² = 1 y = 4(x - 5)² - 1 y = 4((x - 5)(x - 5)) - 1 y = 4(x² - 5x - 5x + 25) - 1 y = 4(x² - 10x + 25) - 1 y = 4(x²) - 4(10x) + 4(25) - 1 y = 4x² - 40x + 100 - 1 y = 4x² - 40x + 99 4x² - 40x + 99 = 0 x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u> 2(4) x = <u>40 +/- √(1600 - 1584)</u> 8 x = <u>40 +/- √(16)</u> 8 x = <u>40 +/- 4</u> 8 x = 5 +/- 1/2 x = 5 + 1/2 x = 5 - 1/2 x = 5 1/2 x = 4 1/2 y = 4x² - 40x + 99 y = 4(5 1/2)² - 40(5 1/2) + 99 y = 4(30 1/4) - 220 + 99 y = 121 - 220 + 99 y = -99 + 99 y = 0 (x, y) = (5 1/2, 0) or y = 4x² - 40x + 99 y = 4(4 1/2)² - 40(4 1/2) + 99 y = 4(20 1/4) - 180 + 99 y = 81 - 180 + 99 y = -99 + 99 y = 0 (x, y) = (4 1/2, 0) <u>y-intercept</u> y = 4x² - 40x + 99 y = 4(0)² - 40(0) + 99 y = 4(0) - 0 + 99 y = 0 - 0 + 99 y = 0 + 99 y = 99 (x, y) = (0, 99) -------------------------------------------------------------------------------------------- <u>vertex</u> y = (x - 1)² = 2 y = (x - 1)² - 2 y = ((x - 1)(x - 1)) - 2 y = (x² - x - x + 1) - 2 y = x² - 2x + 1 - 2 y = x² - 2x - 1 x² - 2x - 1 = 0 x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u> 2(1) x = <u>2 +/- √(4 + 4)</u> 2 x = <u>2 +/- √(8)</u> 2 x = <u>2 +/- 2.83</u> 2 x = 1 +/- 1.415 x = 1 + 1.415 x = 1 - 1.415 x = 2.415 x = 0.415 y = x² - 2x - 1 y = (2.145)² - 2(2.145) - 1 y = 4.60125 - 4.029 - 1 y = 0.57225 - 1 y = 0.42775 (x, y) = (2.415, 0.42775) or y = x² - 2x - 1 y = (0.415)² - 2(0.415) - 1 y = 0.172225 - 0.83 - 1 y = -0.657775 - 1 y = -1.657775 (x, y) = (0.415, -1.657775) <u>y-intercept</u> y = x² - 2x - 1 y = (0)² - 2(0) - 1 y = 0 - 0 - 1 y = 0 - 1 y = -1 (x, y) = (0, -1)