Graph each quadratic function: 1.  f(x)
= 3x2 – 6x – 2 2.  f(x)
= -2(x + 3)(x – 1)
3.  f(x)
= ½(x + 2)2 – 3 Algebra II
1
Quadratics with
Algebra II
2
y
¡ 
Vertex form: x = a(y – k)2 + h
¡  A
Algebra II
parabola that opens left or right
3
¡  Vertex
¡ 
¡ 
¡ 
form: x = a(y –
2
k)
+ h
Vertex: (same as h, opposite of k)
Axis of symmetry (AOS): y = opposite of k
a: determines the direction the graph opens, and the
width of the graph
§  a > 0 opens right
§  a < 0 opens left
§  |a| < 1 wider than x2
§  |a| > 1 narrower than x2
§  |a| = 1 same width as x2
Algebra II
4
x = 2(y+3)2 - 2 Opens right
Shift down 3 Shift Left 2
skinnier Algebra II
5
x = -(y+1)2 + 5 Opens left
Shift down 1 Shift right Same width Algebra II
6
x = ½ (y - 5)2 + 7 Opens right
Shift up 5 Shift right 7
wider
Algebra II
7
Graph:
x = - ½(y + 3)2 + 4
Opens left
Wider than y2
Vertex: (4, -3)
AOS: y = 4
Table à
Reflect
Algebra II
X
Y
8
Graph:
x = 2(y – 1)2 + 3
Opens right
Narrower than y2
Vertex: (3,1)
AOS: y = 1
Table à
Reflect
Algebra II
X
Y
9
Graph:
x = -(y + 5)2 + 2
Opens left
Same width as y2
Vertex: (2, -5)
AOS: y = -5
Table à
Reflect
Algebra II
x
y
10
Graph:
x = 2(y – 1)2 + 1
Opens right
Narrower than x2
Vertex: (1,1)
AOS: y = 1
Table à
Reflect
Algebra II
x
Y
11
Graph:
x = -2(y + 2)2
Opens left
Narrower than y2
Vertex: (0, -2)
AOS: y = -2
Table à
Reflect
Algebra II
x
y
12