Shortcut: Vertex formula

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  1. Applying the "vertex formula" to find the vertex
    Find the vertex for the quadratic function y=2x212x+10y = 2{x^2} - 12x + 10
    1. Converting general form into vertex form by applying the vertex formula
      Convert each quadratic function from general form to vertex form by using the vertex formula.
      1. y=2x212x+10y = 2{x^2} - 12x + 10
      2. y=3x260x50y = - 3{x^2} - 60x - 50
      3. y=12x2+x52y = \frac{1}{2}{x^2} + x - \frac{5}{2}
      4. y=5xx2y = 5x - {x^2}
    2. Deriving the Vertex Formula
      Derive the vertex formula by completing the square:
      \therefore vertex: [b2a,(b24ac)4a][\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]