Chapter 5: Quadratic Functions
(Additional Practice – page 945-947)
FDCSD Standards & Benchmarks
M3:
Uses basic and advanced procedures while performing the process of computation.
M3.38 Add, subtract, multiply, divide, complex numbers
M8: Understands and applies basic and advanced properties of functions and algebra.
M8.32 Fits a line or curve to a set of data and uses this line or curve to make
predictions
M8.34 Uses a variety of algebraic and graphical methods to solve polynomial sentences
with real and complex roots
M8.39 Represents problems using algebraic functions and graphs of those functions
M8.42 Solves quadratic sentences, direct, inverse, joint variations
M8.43 Solves equations with rational expressions
M8.58 Identifies the properties of the graphs of quadratic functions
For the following functions, find the vertex, axis of symmetry, real roots y-intercept and
whether the graph opens up or down.
28) y = !
3
5
(
() (
)
2
x ! 4 +3
)(
29) f x = 3 x + 2 x ! 6
)
(x ! 4) + 3 vertex:( 4,3)
5
vertex:(2,-48)
3
!2
+
6
x
!
4
=
3
( )
axis of sym:x=4
x=
=2
5
2
axis of sym:x=2
!
#
realroots:
4+
5,0
x
!
4
=
5
f
2
=
3
2
+
2
2
!
6
( )
) ( ) realroots:(-2,0)
"
$ ( ) (
x !4=± 5
= 3 ( 4 ) ( !4 )
! 4- 5,0#
%
&
6,0
0=!
3
2
2
2
x = 4± 5
2
3
y = ! 0!4 +3
5
33
y=!
5
(
)
"
!
33 #
y-int:% 0,- &
5$
"
Opens down
$
= !48
() (
)(
f 0 = 3 0+2 0!6
= !36
-8-
( )
) y-int:( 0,-36)
Opens up
Created 12/08
()
29) y = ! x 2 + 7 x ! 12
30) f x = 3x 2 + 4x + 7
0 = 3x 2 + 4x + 7
0 = ! x 2 + 7 x ! 12
0 = x 2 ! 7 x + 12
(
)(
0= x !3 x !4
x=
3+ 4
=
7
x=
! 7 1$
vertex:# , &
" 2 4%
)
axis of sym:x=
x=
7
( )
()
2
()
y = !12
()
2 3
!4 ± !68
6
no real roots
!4
2
x=
=!
6
3
2
" 2%
" 2%
y = 3$ ! ' + 4 $ ! ' + 7
# 3&
# 3&
2
2
2
2
" 7%
" 7%
y = ! $ ' + 7 $ ' ! 12 realroots: 3,0
# 2&
# 2&
4,0
1
y=
4
y-int: 0,-12
y = ! 0 + 7 0 ! 12
( )( )
!4 ± 42 ! 4 3 7
( )
( )
y =5
Opens down
" 2 2%
vertex:$ ! ,5 '
# 3 3&
2
axis of sym:x=3
realroots:none
( )
y-int: 0,7
Opens up
2
3
() ()
2
()
f 0 =3 0 +4 0 +7
=7
31) Write the equation of the parabola you would get by translating the parabola y = x 2 3
units up and 5 units to the left.
( )
2
y= x+5 +3
Factor the following quadratics completely.
12x 2 ! 27
(
32) 3 4x 2 ! 9
(
x 2 + 14x + 49
)
)(
3 2x-3 2x+3
)
33)
5x 2 + 25x + 30
(
34) 5 x 2 + 5x + 6
)
( )( )
35)
5 x+2 x+3
-9-
( )( ) ( )
x+7 x+7 = x+7
2
12x 2 ! 25x ! 7
(3x-7 )( 4x+1)
Created 12/08
Simplify the following expressions.
36)
(3 + 2i ) + (5 ! 7i )
8-5i
37)
-3+3i
(5 ! 2i )(3 ! 7i )
( 3 + 7i ) ( 3 ! 7i )
(3 + 2i )( 4 ! 5i )
2
38) 12 ! 15i + 8i ! 10i
12 ! 7i + 10
(2 ! 3i ) ! (5 ! 6i )
39)
15 ! 35i ! 6i + 14i 2
9 ! 49i 2
15 ! 41i ! 14
22-7i
9 + 49
=
1-41i
58
Solve the following equations over the set of complex numbers.
(
x 2 + 11x + 24 = 0
40)
(x + 3)(x + 8) = 0
)
2
4 x + 6 = 160
41)
( x + 6)
2
= 40
x + 6 = ± 40 = ±2 10
x=-3 or x=-8
x=-6±2 10
10x 2 + 8x ! 1 = 0
4x 2 + 6x + 7 = x 2 ! 4x
3x 2 + 10x + 7 = 0
42)
(3x + 7 ) (x + 1) = 0
x=
42)
3x + 7 = 0 or x + 1 = 0
x=-
7
3
x=
( )( )
2 (10 )
!8 ± 82 ! 4 10 !1
!8 ± 104
20
=
!8 ± 2 26
20
-4± 26
x=
10
or x=-1
- 10 -
Created 12/08