SME
Grade 11 Math · Algebra 2
Parent functions and transformations: shifts, stretches and reflections
Use this for “How is y = 2|x − 3| − 1 moved and stretched from y = |x|? What is y at x = 5?”
Chart
Vertex (3, −1), axis of symmetry x = 3
f(5) = 3
The parent y = |x| is dashed
This is an example. Type your own values to start a new problem.
y
=
a
|
x
−
h
|
+
(
k
)
Formulas
y
=
a
×
|
x
−
h
|
+
k
3 = 2 × |5 − 3| + (−1)
Assumptions
•
Here f(x) = |x|, the dashed parent; h moves the graph right when h is positive, because x − h = 0 at x = h.
•
k moves it up; a stretches it by a factor of |a| and flips it over the x-axis when a is negative.
•
The parent’s vertex (0, 0) lands at (h, k).
Step-by-step
WE KNOW
a = 2, h = 3, k = −1, x = 5
FIND
output (y)
Step 1 · Find output (y)
Use y = a × |x − h| + k
Shift
x
by
h
,
take
the
absolute
value,
stretch
by
a
,
then
shift
up
by
k
.
y
=
2
×
|5
−
3|
−
1
y
=
2
×
2
−
1
y
=
4
−
1
y
=
3
Check
Put the numbers back in. Both sides should match.
3 = 2 × |5 − 3| − 1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.