Shortcut: Vertex formula

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Examples
Lessons
  1. Applying the "vertex formula" to find the vertex
    Find the vertex for the quadratic function y=2x2−12x+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=2x2−12x+10y = 2{x^2} - 12x + 10
      2. y=−3x2−60x−50y = - 3{x^2} - 60x - 50
      3. y=12x2+x−52y = \frac{1}{2}{x^2} + x - \frac{5}{2}
      4. y=5x−x2y = 5x - {x^2}
    2. Deriving the Vertex Formula
      Derive the vertex formula by completing the square:
      y=ax2+bx+cy=ax^2+bx+c
      :
      :
      (y+(b2−4ac)4a)=a(x+b2a)(y+\frac{(b^2-4ac)}{4a})=a(x+\frac{b}{2a})
      ∴\therefore vertex: [−b2a,−(b2−4ac)4a][\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]