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Unit 8 Test Review
A high diver jumps off a diving platform. The equation that represents the path of the diver is
y = -4.9x² + 8x + 10 where x is the time in seconds and y is the height above the water’s
surface in meters.
1. Draw and label a graph of the situation. Give the window used.
WINDOW:
Xmin:__-1_____
Xmax:__3_____
Xscl:___1_____
Ymin:___-5____
Ymax:__15____
Yscl:____1_____
2. Where is the diver at 1.5 sec?
________10.98 m_______
3. Where is the diver at 2 sec?
_______6.4 m________
4. At what time is the diver 8 meters above the water’s surface?
_________1.85 s_______
5. At what time is the diver 1 meter above the water’s surface?
______2.40 s__________
6. At what time does the diver hit the water’s surface?
________2.46 s________
7. What is the height of the diver when she hits the water?
_____0 m_____________
8. What is the maximum height of the diver?
________13.27 m_______
9. When does the diver reach the maximum height?
______0.82 s__________
10. What is the domain for this problem?
______[0, 2.46]_________
11. What is the range for this problem?
______[0, 13.27]________
12. Two numbers have a difference of 3 and a product of 1890. What number sets have both of
these properties?
42, 45; -45, -42
A rectangular pen is made with 280m of fencing.
13. Label the dimensions on the diagram. Let x = the shorter side.
(6 points)
14. Express the area as a function of the length and the width. A(x) = _x(140-x) _______
(6 points)
15. Enter the function into the calculator and sketch a graph of the function in an appropriate viewing
window. (10 points)
WINDOW:
Xmin:___0_____ Ymin:__0_____
Xmax:__160___
Ymax:__5000___
Xscl:____5____
Yscl:__50_____
16. Find the maximum area of the pen. (5 points)
_________4900___________
17. Find the dimensions which will give this maximum area.
(6 points)
_w = 70 l = 70_____________
18. Solve this system:
𝑦 + 3𝑥 = 0
𝑦 − 6 = 3𝑥 2
No solution
19. Solve this system:
4, 8
1
𝑦 + 2 = 4 (𝑥 − 4)2
𝑥−𝑦=6
Quadratic Inequalities Match-up
Problem
20.
21.
22.
23.
24.
25.
26.
27.
x2 – x – 6 < 0
x2 + 7x + 6 > 0
2x2 + 7x – 4 > 0
–x2 + x + 6 < 0
2x2 – 5x – 3 < 0
x2 + 3x – 4 > 0
4x2 – 9 < 0
–x2 – 7x – 6 > 0
Graph #
Letter
Symbol
8
4
5
1
2
6
3
7
B
A
H
D
E
G
C
F
TRIANGLE
HEART
ARROW
PLUS
CHECK
DIAMOND
RECTANGLE
STAR
Answer selections are on the next three pages
1
2
3
4
5
6
7
8
A
B
+
+
+
-
-6
+
-
-2
-1
C
3
D
+
+
+
-3
2
-
-
-2
3
2
E
3
F
+
+
-1
2
+
-
-
3
-6
G
-1
H
+
+
-4
-
1
+
+
-4
½
♦
-6 < x < -1
(-6,-1)
x < -4 or x > 1
(-2,3)
-2 < x < 3
x < -2 or x > 3
▲
( 1 ,3)
2
 1 x3
2
x < -4 or x > 1
2
♥
■
♥
■
x < -6 or x > -1
( 3, 3 )
2 2
 3  x 3
2
2