Algebra II with Trigonometry
Name
Pd.
UNIT QF STUDY GUIDE
TEST: FRIDAY 11/21
Solve by factoring.
1)
50x2 – 200 = 0
2)
8x2 = 56x
3)
18x3 – 2x2 + 36x = 4
4)
36x2 + 33x - 15 = 0
Solve by finding the square root.
5)
x2 – 98 = 0
6)
-x2 + 2 = x2 + 14
7)
5x2 – 8 = 4
8)
3 2
x + 6 = 18
4
Solve by completing the square.
9)
x2 + 3x – 2 = 0
GD/MPH/RS 1/09
10) 4x2 – 16x = 10
1
Algebra II with Trigonometry
Solve using the Quadratic Formula.
11) 6x2 - 19x - 7 = 0
12) 11 = -3x2 – 7x
Use the discriminant to determine the nature of the roots for each quadratic
equation.
Equation
Value of the
Discriminant
Number of Roots
Real or
Imaginary Roots
13) 6x2 – x + 1 = 0
14) x2 – 2 = -6x
15) -14x2 -12x = 4
16) 9x2 – 12x + 4 = 0
GD/MPH/RS 1/09
2
Algebra II with Trigonometry
Graph each quadratic equation. State the vertex, axis of symmetry, x- and yintercepts, and if the graph opens up or down.
17) y = x2 - 2x + 1
18) y = 2x2 + 8x
19) y = -x2 + 6x - 10
20) y >
GD/MPH/RS 1/09
1 2
x -4
3
3
Algebra II with Trigonometry
Rewrite each equation in vertex form and identify the vertex and axis of symmetry.
21) f(x) = x2 - 8x + 11
22) f(x) = -x2 - 10x
23) f(x) = 2x2 + 24x - 7
24) f(x) = -5x2 + 30x + 2
Solve each of the following word problems. Round to tenths as appropriate.
25) The length of a rectangle is 8 cm less than three times its width. If the area of the
rectangle is 476 cm2, find the dimensions of the rectangle.
26) The longer leg of a right triangle is 6 units more than twice the shorter leg. If the
hypotenuse is 3 units longer than longer leg, find the dimensions of the right
triangle.
27) While standing on the observation deck of the Space Needle (which is 520 feet
above the ground), Stanley is debating whether or not to release his ice cream cone
on the unsuspecting crowd below. How long will it take the ice cream cone to hit the
ground if:
a)
he drops the cone?
GD/MPH/RS 1/09
b)
he throws the cone up at 40 ft/s?
4
Algebra II with Trigonometry
ANSWERS (Match answers to Questions #1 - 12)
A.
±4
B.
C.
±7 2
D.
E.
0, 7
F.
G.
-2, 2
H.
I.
2±
K.
26
2
2 15
±
5
3 ± 17
2
1
, ± 2i
9
-1 7
,
3 2
± 6i
J.
L.
Question
13
14
15
16
Value of the
Discriminant
-23
44
-80
0
-5 1
,
4 3
-7 ± 83i
6
Number of
Roots
2
2
2
1
Real or Imaginary
Roots
imaginary
real
imaginary
real
GRAPHS
Question
Vertex
17
18
19
20
(1, 0)
(-2, -8)
(3, -1)
(0, -4)
21)
22)
23)
24)
f(x)
f(x)
f(x)
f(x)
= (x-4)2 – 5
= -(x+5)2 + 25
= 2(x+6)2 – 79
= -5(x-3)2 + 42
25) 14 cm by 34 cm
27A) 5.7 seconds
GD/MPH/RS 1/09
Axis of
Symmetry
x=1
x = -2
x=3
x=0
x-intercept(s)
y-intercept
(1, 0)
(0, 0), (-4, 0)
none
( 2 3 , 0)
(0, 1)
(0, 0)
(0, -10)
(0, -4)
vertex (4, -5)
vertex (-5, 25)
vertex (-6, 79)
vertex (3, 42)
Opens Up
or Down
up
up
down
up
AOS x = 4
AOS x = -5
AOS x = -6
AOS x =3
26) 15, 36, 39
27B) 7.9 seconds
5