Section 5.1
The Parabola
433
Version: Fall 2007
5.1
Exercises
In
Exercises 1

6
, sketch the image of
your calculator screen on your homework
paper.
Label and scale each axis with
xmin, xmax, ymin, and ymax.
Label
each graph with its equation.
Remember
to use a ruler to draw all lines, including
axes.
1.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =
x
2
,
g
(
x
) = 2
x
2
, and
h
(
x
) = 4
x
2
on one screen. Write a short
sentence explaining what you learned in
this exercise.
2.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =

x
2
,
g
(
x
) =

2
x
2
,
and
h
(
x
) =

4
x
2
on one screen. Write a
short sentence explaining what you learned
in this exercise.
3.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =
x
2
,
g
(
x
) = (
x

2)
2
, and
h
(
x
) = (
x

4)
2
on one screen.
Write a short sentence explaining what
you learned in this exercise.
4.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =
x
2
,
g
(
x
) = (
x
+
2)
2
, and
h
(
x
) = (
x
+ 4)
2
on one screen.
Write a short sentence explaining what
you learned in this exercise.
5.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =
x
2
,
g
(
x
) =
x
2
+
2
, and
h
(
x
) =
x
2
+ 4
on one screen.
Write a short sentence explaining what
you learned in this exercise.
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1
6.
Use your graphing calculator to sketch
the graphs of
f
(
x
) =
x
2
,
g
(
x
) =
x
2

2
, and
h
(
x
) =
x
2

4
on one screen.
Write a short sentence explaining what
you learned in this exercise.
In
Exercises 7

14
, write down the given
quadratic function on your homework pa
per, then state the coordinates of the ver
tex.
7.
f
(
x
) =

5(
x

4)
2

5
8.
f
(
x
) = 5(
x
+ 3)
2

7
9.
f
(
x
) = 3(
x
+ 1)
2
10.
f
(
x
) =
7
5
x
+
5
9
2

3
4
11.
f
(
x
) =

7(
x

4)
2
+ 6
12.
f
(
x
) =

1
2
x

8
9
2
+
2
9
13.
f
(
x
) =
1
6
x
+
7
3
2
+
3
8
14.
f
(
x
) =

3
2
x
+
1
2
2

8
9
In
Exercises 15

22
, state the equation
of the axis of symmetry of the graph of
the given quadratic function.
15.
f
(
x
) =

7(
x

3)
2
+ 1
16.
f
(
x
) =

6(
x
+ 8)
2
+ 1
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434
Chapter 5
Quadratic Functions
Version: Fall 2007
17.
f
(
x
) =

7
8
x
+
1
4
2
+
2
3
18.
f
(
x
) =

1
2
x

3
8
2

5
7
19.
f
(
x
) =

2
9
x
+
2
3
2

4
5
20.
f
(
x
) =

7(
x
+ 3)
2
+ 9
21.
f
(
x
) =

8
7
x
+
2
9
2
+
6
5
22.
f
(
x
) = 3(
x
+ 3)
2
+ 6
In
Exercises 23

36
, perform each of the
following tasks for the given quadratic
function.
i.
Set up a coordinate system on graph
paper. Label and scale each axis.
ii.
Plot the vertex of the parabola and
label it with its coordinates.
iii. Draw the axis of symmetry and label
it with its equation.
iv. Set up a table near your coordinate
system that contains exact coordinates
of two points on either side of the axis
of symmetry. Plot them on your co
ordinate system and their “mirror im
ages” across the axis of symmetry.
v.
Sketch the parabola and label it with
its equation.
vi. Use interval notation to describe both
the domain and range of the quadratic
function.
23.
f
(
x
) = (
x
+ 2)
2

3
24.
f
(
x
) = (
x

3)
2

4
25.
f
(
x
) =

(
x

2)
2
+ 5
26.
f
(
x
) =

(
x
+ 4)
2
+ 4
27.
f
(
x
) = (
x

3)
2
28.
f
(
x
) =

(
x
+ 2)
2
29.
f
(
x
) =

x
2
+ 7
30.
f
(
x
) =

x
2
+ 7
31.
f
(
x
) = 2(
x

1)
2

6
32.
f
(
x
) =

2(
x
+ 1)
2
+ 5
33.
f
(
x
) =

1
2
(
x
+ 1)
2
+ 5
34.
f
(
x
) =
1
2
(
x

3)
2

6
35.
f
(
x
) = 2(
x

5
/
2)
2

15
/
2
36.
f
(
x
) =

3(
x
+ 7
/
2)
2
+ 15
/
4
In
Exercises 37

44
, write the given qua
dratic function on your homework pa
per, then use setbuilder and interval no
tation to describe the domain and the
range of the function.
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