QUADRATIC RELATIONS
(from y = x2 to y = a(x – h)2 + k)
SUMMARY:
y = a(x – h)2 + k
 vertical stretch
(a > 1)
 vertical compression
(0 < a < 1)
 reflection (x-axis)
(a = –1)
Example 1:
 horizontal translation
(+) move left
(–) move right
 vertical translation
(+) move up
(–) move down
Consider the given parabola:
a)
Identify the coordinates of the vertex.
b)
State the values of h and k.
h=
k=
c)
Is the value of a positive or negative?
d)
Determine the value of a.
a=
e)
Write an equation for the parabola
in the form y = a(x – h)2 + k.
Example 2:
The parabola y = x2 is transformed. Write the equation of each
transformed parabola in the form y = a(x  h)2 + k.
a)
vertically stretched by a factor of 3, reflected in the
x-axis, and translated 5 units left and 1 unit down; _________________
b)
vertically compressed by a factor of ½ and
translated 3 units right and 5 units up.
Unit 2 Lesson4
_________________
Page 1 of 2
Example 3:
Complete the following table:
Function
Vertex
Axis of
Relation to y = x2
Symmetry (narrower/wider)
Direction of
Opening
Max or Min
Value
1
y = (x – 4)2 + 3
2
y = –3(x + 5)2 – 2
Example 4:
Sketch each of the following parabolas on the same set of axes:
1
 y = x2
 y = (x – 4)2 + 3
 y = –3(x + 5)2 – 2
2
Homework:
p.212–214
#1abfh, 2cegh, 4acd
Unit 2 Lesson4
Page 2 of 2