# 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 $y = 2{x^2} - 12x + 10$
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. $y = 2{x^2} - 12x + 10$
2. $y = - 3{x^2} - 60x - 50$
3. $y = \frac{1}{2}{x^2} + x - \frac{5}{2}$
4. $y = 5x - {x^2}$
2. 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: $[\frac{-b}{2a} ,\frac{-(b^2-4ac)}{4a} ]$
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