Section 5.4
The Quadratic Formula
497
Version: Fall 2007
5.4
Exercises
In
Exercises 1

8
, find all real solutions
of the given equation. Use a calculator to
approximate the answers, correct to the
nearest hundredth (two decimal places).
1.
x
2
= 36
2.
x
2
= 81
3.
x
2
= 17
4.
x
2
= 13
5.
x
2
= 0
6.
x
2
=
−
18
7.
x
2
=
−
12
8.
x
2
= 3
In
Exercises 9

16
, find all real solutions
of the given equation. Use a calculator to
approximate your answers to the nearest
hundredth.
9.
(
x
−
1)
2
= 25
10.
(
x
+ 3)
2
= 9
11.
(
x
+ 2)
2
= 0
12.
(
x
−
3)
2
=
−
9
13.
(
x
+ 6)
2
=
−
81
14.
(
x
+ 7)
2
= 10
15.
(
x
−
8)
2
= 15
16.
(
x
+ 10)
2
= 37
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1
In
Exercises 17

28
, perform each of the
following tasks for the given quadratic
function.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
Remember to draw all lines with
a ruler.
ii.
Place the quadratic function in ver
tex form. Plot the vertex on your co
ordinate system and label it with its
coordinates.
Draw the axis of sym
metry on your coordinate system and
label it with its equation.
iii. Use the quadratic formula to find the
x
intercepts of the parabola.
Use a
calculator to approximate each inter
cept, correct to the nearest tenth, and
use these approximations to plot the
x
intercepts on your coordinate sys
tem. However, label each
x
intercept
with its
exact
coordinates.
iv. Plot the
y
intercept on your coordi
nate system and its mirror image across
the axis of symmetry and label each
with their coordinates.
v.
Using all of the information on your
coordinate system, draw the graph of
the parabola, then label it with the
vertex form of the function. Use in
terval notation to state the domain
and range of the quadratic function.
17.
f
(
x
) =
x
2
−
4
x
−
8
18.
f
(
x
) =
x
2
+ 6
x
−
1
19.
f
(
x
) =
x
2
+ 6
x
−
3
20.
f
(
x
) =
x
2
−
8
x
+ 1
21.
f
(
x
) =
−
x
2
+ 2
x
+ 10
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498
Chapter 5
Quadratic Functions
Version: Fall 2007
22.
f
(
x
) =
−
x
2
−
8
x
−
8
23.
f
(
x
) =
−
x
2
−
8
x
−
9
24.
f
(
x
) =
−
x
2
+ 10
x
−
20
25.
f
(
x
) = 2
x
2
−
20
x
+ 40
26.
f
(
x
) = 2
x
2
−
16
x
+ 12
27.
f
(
x
) =
−
2
x
2
+ 16
x
+ 8
28.
f
(
x
) =
−
2
x
2
−
24
x
−
52
In
Exercises 29

32
, perform each of the
following tasks for the given quadratic
equation.
i.
Set up a coordinate system on a sheet
of graph paper. Label and scale each
axis.
Remember to draw all lines with
a ruler.
ii.
Show that the discriminant is nega
tive.
iii. Use the technique of completing the
square to put the quadratic function
in vertex form.
Plot the vertex on
your coordinate system and label it
with its coordinates. Draw the axis of
symmetry on your coordinate system
and label it with its equation.
iv. Plot the
y
intercept and its mirror
image across the axis of symmetry
on your coordinate system and label
each with their coordinates.
v.
Because the discriminant is negative
(did you remember to show that?),
there are no
x
intercepts.
Use the
given equation to calculate one addi
tional point, then plot the point and
its mirror image across the axis of
symmetry and label each with their
coordinates.
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 Quadratic Formula, Quadratic equation, real solutions

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