QUADRATIC RELATIONS
(from y = x2 to y = a(x – h)2)
Example 1:
Sketch each of the following parabolas on the same set of axes:
 y = x2
 y = (x – 2)2
 y = (x + 3)2
Complete the following table:
Function
Value of h in
y = (x – h)2
Relation to y = x2
(left/right)
Vertex
Axis of Symmetry
y = (x – 2)2
y = (x + 3)2
In general, a HORIZONTAL TRANSLATION is given by
y = (x – h)2
if h > 0 the horizontal shift is RIGHT
if h < 0 the horizontal shift is LEFT
Example 2:
Suppose each pair of relations were graphed on the same set of axes.
Which parabola would be the widest (most vertically compressed)?
Which parabola would have its vertex farther from the y-axis?
a) y =
1
( x  3)2 and y = –5(x + 4)2
2
b) y = 2(x + 3)2 and y = 3(x – 2)2
Widest?
_____________
Farthest? _____________
Widest?
_____________
Farthest? _____________
Unit 2 Lesson3
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Example 3:
Sketch each of the following parabolas on the same set of axes:
 y = x2
Example 4:
 y = –2(x + 4)2
 y=
1
( x  3)2
2
Describe the shape and position of each of the following parabolas
relative to y = x2:
1
a) y = –2(x + 1)2
b) y = ( x  2)2
3
Homework: p.200–201 #2 (don’t graph), 5
Graph:
Unit 2 Lesson3
y = x2
y = –(x + 5)2
y = 3(x – 1)2
1
y = ( x  2)2
2
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