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Name: ____________ Date: ____________ Quadratic Equations Solve each equation. x2 + ax + b = c 1. x2 + 6x + 9 = 16 2. x2 - 4x + 4 = 25 (x + 3)2 = 16 x+3=±4 x=±4-3 x = -7, 1 3. 5. 7. 9. Page 10 x2 - 6x + 9 = 36 x2 - 10x + 25 = 16 x2 - 12x + 36 = 81 x2 - 14x + 49 = 100 4. 6. 8. 10. x2 + 8x + 16 = 49 x2 + 4x + 4 = 64 x2 - 8x + 16 = 25 x2 + 16x + 64 = 36 Copyright © 2006-2016 MathPlus® P Name: ____________ Date: ____________ Quadratic Equations Solve each equation using the FOIL method. x2 + 2x - 3 = 0 1. 1 1 1 -1 +3 2. x2 - x - 20 = 0 -3 3-1=2 (x - 1)(x + 3) = 0 x = -3, 1 3. x2 - 8x + 12 = 0 4. x2 - 2x - 63 = 0 5. x2 - 9x + 14 = 0 6. x2 - 9x - 22 = 0 7. x2 - 14x + 48 = 0 8. x2 - 12x + 27 = 0 9. x2 - 6x - 40 = 0 10. x2 - 6x + 5 = 0 Page 21 Copyright © 2006-2016 MathPlus® P Name: ____________ Date: ____________ Quadratic Equations Answer the following questions based on the graphs on previous 5 pages. From To Result y = x2 y = -x2 parabola turns upside down y = x2 y = (x - 3)2 axis of symmetry moves from x = 0 to x = ___ y = (x - 3)2 y = -(x - 3)2 parabola turns ________________ y = (x - 3)2 y = (x - 3)2 + 1 parabola moves ______ (up or down) by 1 2 3 4 _______ (number of units) 5 y = x2 y = 2x2 Parabola becomes _____________ (wider or narrower) 6 y = x2 y = (1/3)x2 Parabola becomes _____________ (wider or narrower) 7 y = (1/3)x2 y = (1/3)(x - 5)2 axis of symmetry moves from x = _____ to x = _____ 8 y = -(x - 1)2 y = -(x - 1)2 - 3 parabola moves ______ (up or down) by _______ (number of units) Page 62 Copyright © 2006-2016 MathPlus® P Name: ____________ Date: ____________ Quadratic Equations Graphing by finding and using the axis of symmetry and vertex. 1. x = y2 + 2y + 5 2. x = y2 + 4y + 10 Completing the square: x = y2 + 2y + 1 + 4 = (y + 1)2 + 4 axis of symmetry: y = -1 3. x = 4y2 + 8y - 3 axis of symmetry: 5. axis of symmetry: 4. vertex = x = -2y2 - 4y + 7 axis of symmetry: Page 89 vertex = (4, -1) vertex = x = -y2 + 4 axis of symmetry: 6. vertex = vertex = x = 3y2 + 12y + 5 axis of symmetry: Copyright © 2006-2016 MathPlus® vertex = P Name: ____________ Date: ____________ Quadratic Equations Determine the quadratic equation of the graph. 1. 2. 2 -4 2 -5 y= 3. 1 (x - 2) 2 2 x=4 4. x = -2 1 6 -3 Page 108 (-5, -4) Copyright © 2006-2016 MathPlus® P Name: ____________ Date: ____________ Quadratic Equations Graph Inequality Example : y (x + 2)2 - 4 try point (-2, 0): 0 (-2 + 2) - 4 0 -4, this is true. Therefore, the answer is the shaded area inside the parabola. Since the answer includes the parabola itself, solid line is used for the curve. y = (x + 2)2 - 4 (-2, 0) Example : y < x2 - 8x + 12 y < x2 - 8x + 16 - 4 y < (x - 4)2 - 4 try point (4, 0): 0 < (4 - 4)2 - 4 0 < -4, this is NOT true. Therefore, the answer is the shaded area outside the parabola. Since the answer doesn’t include the parabola itself, dotted line is used. y = (x - 4)2 - 4 (4, 0) Page 114 Copyright © 2006-2016 MathPlus® P