# Shortcut: Vertex formula

### 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: $[\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]$