2.1 Transformations of Parabolas 10/12/2012
Feb 22, 2016
2.1 Transformations of Parabolas
10/12/2012
Graph is a parabola
VocabularyQuadratic Function :
a function that is written in the standard form: ax2 + bx + c where a ≠ 0
Vertex: The highest or lowest point of the parabola.
Vertex
Vertex
the line that divides a parabola into mirror images and passes through the vertex.
Axis of symmetry:
Axis of symmetry
Graph y = x2
Simplest quadratic equation
xxx
-2
-1
0
1
2
y
4
1
0
1
4
Graph y = -x2
xxx
-2
-1
0
1
2
y
-4
-1
0
-1
-4 Note: Graph is reflected in the x-axis.
Graph y = 2x2
xxx
-2
-1
0
1
2
y
8
2
0
2
8Note: Graph is stretched vertically by a factor of 2.
Graph y = x2
xxx
-2
-1
0
1
2
y
2
½
0
½
2Note: Graph shrinks vertically by factor of ½
Graph y = (x-2)2
xxx
0
1
2
3
4
y
4
1
0
1
4Note: Graph shifts 2 units to the right.
Graph y = (x+2)2
xxx
-4
-3
-2
-1
0
y
4
1
0
1
4Note: Graph shifts 2 units to the left.
Graph y = x2 - 2
xxx
-2
-1
0
1
2
y
2
-1
-2
-1
2Note: Graph shifts 2 units down.
Graph y = x2 + 2
xxx
-2
-1
0
1
2
y
6
3
2
3
6Note: Graph shifts 2 units up.
Graph y = (x-2)2 + 4
xxx
0
1
2
3
4
y
8
5
4
5
8Note: Graph shifts 2 units to the right and 4 units up.
Graph y = -½(x+2)2-2
Graph shrinks vertically by ½ and is reflected in
the x-axis
Graph shifts 2 units to the left.
Graph shifts 2 units down