Download Algebra II Test Unit Five – Quadratic Functions Good Luck To NON

Algebra II Test
Unit Five – Quadratic Functions
Good Luck To______________________________________________Period_____Date______________
NON-CALCULATOR SECTION
Vocabulary: Define each word and give an example.
1.
Parabola
2.
Discriminant
3.
Imaginary Unit
Short Answer:
4. Describe how to find the complex conjugate of a complex number. What is the result of the product of a number and its
complex conjugate?
5.
Describe how to factor a trinomial of the form a  2ab  b .
2
2
Review:
3 4
 2 1


6.
Find the inverse of the matrix:
7.
Write an equation in slope-intercept form for the line parallel to  y  3x  6 that passes through the
point
8.
1,5 .
Find
f  4  for f  x  
1 2
x  6x  3 .
2
Problems:
**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**
9.
Simplify:
a.
3 56
b.
3
8
c.
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20
10. Graph the quadratic functions. Label the vertex and axis of symmetry on each graph.
y  2x2  5
a.
b. y    x  1  3
2
c.
y  x2  4x  5
11. Solve the quadratic equations by factoring.
a. x  1  0
2
b. 2 x  4 x  30
c. x  8 x  0
2
2
12. Solve the quadratic equations by square roots.
a. x  1  8
2
b. 4  x  2   16
c. 4 x  48
2
2
13. Solve the quadratic equation by completing the square: x  4 x  2  0
2
14. Solve the quadratic equation by the quadratic formula: 2 x  3 x  4
2
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15. Simplify the following:
a.
9  7i   10  6i 
16. Write
b.
 3  2i  4  3i 
c.
y  x 2  6 x  8 in vertex form. Find the zeros and the vertex of the function.
17. Solve the quadratic inequalities:
a. 25 x  100  0
2
b. 4 x  12 x  0
2
18. Graph the quadratic inequalities:
a.
y  x2  2 x  1
b.
y   x2  5
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3
7i
Multiple Choice Questions: Circle the best answer.
19. Solve the equation x  18 x  81  0 by factoring.
2
A. x  9
B. x  9
C. x  9
D. No solution
20. Which is the solution set for 2 x  7 x  1  0 ?
2
A.
 7  41 7  41 
,


4 
 4
B.
 7  57 7  57 
,


4 
 4
 7  57 7  57 
,


4
4


 7  41 7  41 
,
D. 

4
4


C.
21. Which is the solution set of  6 x  4   77 ?
2
A.
 4  77 4  77 
,


12 
 12
B.
 4  77 4  77 
,


6 
 6
C.
 4  77 4  77 
,


12

 12
D.
 4  77 4  77 
,


6
6


22. Use the discriminant to determine the number and types of solutions of the equation 9 x  30 x  25  0 .
2
A.
B.
C.
D.
no real solution, 2 imaginary solutions
1 real solution, no imaginary solutions
1 real solution, 1 imaginary solution
2 real solutions
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23. Which of the following graphs represents the quadratic inequality
A.
A.
B.
C.
y  x2  4x ?
D.
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Algebra II Test
Unit Five – Quadratic Functions
Good Luck To______________________________________________Period_____Date______________
CALCULATOR SECTION
1.
A geyser sends a blast of boiling water into the air. During the eruption, the height h (in feet) of the water t seconds after being
forced out of the ground could be modeled by h  16t  70t .
2
2.
a.
What is the maximum height of the boiling water?
b.
How long is the boiling water in the air?
From 1990-1993, the number of truck registrations (in millions) in the United States can be approximated by the model
R  0.29t 2  45 , where t is the number of years since 1990. During which year were approximately 46.16 million trucks
registered?
3.
On fourth down, a team is just out of field goal range. The punter is called in to punt. To avoid kicking the ball into the
endzone, the punter needs to kick the football high and short. This punt can be modeled by y  0.088x
x is the distance (in yards) the football is kicked and y is the height (in yards) the football is kicked.
a.
Find the maximum height of the football.
b. If the punter punted the ball from the 40-yard line, did the ball reach the endzone?
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2
 2.5x  1 , where
**Extra Credit: Write a quadratic function in standard form whose graph passes through the given points:
 1, 7 , 1, 5 ,  2, 1
**Extra Credit: Solve the quadratic equation ax  bx  c  0 by completing the square.
2
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