Shortcut: Vertex formula

Lessons

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

---

• 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)

  $y = 2{x^2} - 12x + 10$
  
  
  b)

  $y = - 3{x^2} - 60x - 50$
  
  
  c)

  $y = \frac{1}{2}{x^2} + x - \frac{5}{2}$
  
  
  d)

  $y = 5x - {x^2}$
  
  

---

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

---