Quadratic Equations

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[edit] Factorization

  • Grouping: (ax + ay + bx+ by)
    • = a*(x + y) + b*(x + y)
    • = x*(a + b) + y*(a + b)
    • = (x + y)*(a + b)
  • Quadratic: (ax^2 + bx + c)
    • = (Mx + N)*(Px + Q)
    • MNx^2 + (MQ +NP)x + NQ
    • MP = a; MQ + NP = b; NQ = c


[edit] Quadratic of Perfect Square

  • x^2 + 2bx + b^2 = (x + b)*(x + b) = (x + b)^2


[edit] Null Factor Law

  • a*b = 0, then a = 0, b = 0, or a = 0 = b


[edit] Quadratic Formula

  • (ax + ay + bx+ by) = 0
  • x = (-b ± √(b^2 – 4ac) / (2a)


[edit] Dilation Along The Y-Axis

  • y = ax2
    • A > 1; Stretched Along Y-Axis
    • 0 < a < 1; Shrinks Along Y-Axis
    • 0 < a; Parabola Is Inverted


[edit] Translation

  • Translation Along X-Axis
    • - (h) > 0; Parabola Translated To Right
    • + (h) > 0; Parabola Translated To Left
  • Translation Along Y-Axis
    • - (k) > 0; Parabola Translated Downward
    • + (k) > 0; Parabola Translated Upward


[edit] Turning Point Form

  • Y = a (x – h)2 + k
  • Turning Point = (h, k)
  • Symmetrical when x = h

[edit] The Intercept Method

  • Axis of Symmetry: x = -(b) / (2a)
  • Vertex = Turning Point
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