Objectives:
• Be able to graph a quadratic function in vertex form
• Be able to write a quadratic function in vertex form (2 ways)

Vertex Form of a Quadratic
Parent Function: y
 x
2
Vertex Form of a Quadratic Equation:
( )

(

)
2  k
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
5
4
3
2
1
1 2 3 4 5
Reflection over x -axis if a is negative, vertical stretch ( a > 1) or shrink ( a < 1)
Horizontal translation
Vertical
Translation
(opposite of what you see!)
*The vertex of the parabola is ( h , k ) and the axis of symmetry is x = h .

Graphing Equations in Vertex Form
Ex 1) y
 
1
2
( x

2)
2 
3 a. Vertex (horiz. and vert. translation)
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
10
8
6
4
2
2 4 6 8 10 b. Axis of symmetry c. Table
• Point
•
Vertex
• Corresp.
x d. Ask:
• Correct reflection?
•
Correct stretch or shrink?
y

Vertex Form from Graph
Ex 4) Write the equation for the following parabola in vertex form: y = a ( x – h ) 2 + k

Vertex Form from Standard Form
Ex5) Write y = 2 x 2 + 10 x + 7 in vertex form.
a. Find the x -coordinate of the vertex ( h ) :
 b
2 a b. Find the y -coordinate of the vertex ( k ) : c. Substitute a , h , and k into vertex form: y
 a ( x
 h )
2  k