QUADRATIC RELATIONS
(from y = x2 to y = ax2 + k)
Example 1:
Sketch each of the following parabolas on the same set of axes:
1
 y = x2
 y = 2x2
 y = x2
 y = –x2
2
Complete the following table:
Function
Vertex
Relation to y = x2
(narrower/wider)
Direction of
Opening
Max or Min Value
at Vertex
y = 2x2
1 2
x
2
y = –x2
y=
In general, a VERTICAL STRETCH/COMPRESSION/REFLECTION
is given by
y = ax2
if a > 1 it is a vertical STRETCH by a factor of a
if 0 < a < 1 it is a vertical COMPRESSION by a factor of a
if a < 0 it is a REFLECTION in the x-axis
Unit 2 Lesson 2
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Example 2:
Sketch each of the following parabolas on the same set of axes:
 y = x2
 y = x2 + 4
 y = x2 – 3
Complete the following table:
Function
Value of k in
y = x2 + k
Relation to y = x2
(up/down)
Vertex
Axis of Symmetry
y = x2 + 4
y = x2 – 3
In general, a VERTICAL TRANSLATION is given by
y = x2 + k
if k > 0 the vertical shift is UP
if k < 0 the vertical shift is DOWN
Unit 2 Lesson 2
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Example 3:
Describe the shape and position of each of the following parabolas
relative to y = x2:
1 2
a) y = 3x2 + 5
b) y =
x –2
4
Example 4:
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 x-axis?
a) y =
b) y =
1 2
_______________
x – 2 and y = –3x2 + 5 Widest?
2
Farthest? _______________
1 2
x + 4 and y = 5x2 – 4
3
Widest?
_______________
Farthest? _______________
Example 5:
Sketch each of the following parabolas on the same set of axes:
1 2
 y = x2
 y = 2x2 + 3
 y=
x –2
2
Homework:
p.191–192 #4, 7
(don’t graph)
Graph:
Unit 2 Lesson 2
y = x2
y = x2 – 4
y = –2x2 + 5
1
y = x 2 –2
2
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