Question

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Describe the transformation of the parent function y = x^2 as it relates to the function h (x)
= 1/2(x - 5)^2+ 4

Answer 1

The parent function is the simplest form of the type of function given.
y
=
x
2
y
=
x
2
For a better explanation, assume that
y
=
x
2
y
=
x
2
is
f
(
x
)
=
x
2
f
(
x
)
=
x
2
and
y
=
x
2
y
=
x
2
is
g
(
x
)
=
x
2
g
(
x
)
=
x
2
.
f
(
x
)
=
x
2
f
(
x
)
=
x
2
g
(
x
)
=
x
2
g
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
g
(
x
)
=
x
2
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
The horizontal shift depends on the value of
h
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
h
units.
g
(
x
)
=
f
(
x
−
h
)
g
(
x
)
=
f
(
x
-
h
)
- The graph is shifted to the right
h
h
units.
In this case,
h
=
0
h
=
0
which means that the graph is not shifted to the left or right.