Shortcut: Vertex formula

Shortcut: Vertex formula

Lessons

  • 1.
    Applying the "vertex formula" to find the vertex
    Find the vertex for the quadratic function y=2x212x+10y = 2{x^2} - 12x + 10

  • 2.
    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.
    a)
    y=2x212x+10y = 2{x^2} - 12x + 10

    b)
    y=3x260x50y = - 3{x^2} - 60x - 50

    c)
    y=12x2+x52y = \frac{1}{2}{x^2} + x - \frac{5}{2}

    d)
    y=5xx2y = 5x - {x^2}


  • 3.
    Deriving the Vertex Formula
    Derive the vertex formula by completing the square:
    y=ax2+bx+cy=ax^2+bx+c
    :
    :
    (y+(b24ac)4a)=a(x+b2a)(y+\frac{(b^2-4ac)}{4a})=a(x+\frac{b}{2a})
    \therefore vertex: [b2a,(b24ac)4a][\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]