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Math 2
The Great Quadratic Unit Pre-Assessment
Name _________________________
Period _____
MM2N1. Students will represent and operate with complex numbers.
_____ 1. Find the product:
3  6i  4  7i 
a) 12  42i
b) 30  45i
_____ 2. Which is the value of i18 ?
a) 1
b) -1
_____ 3. What is the conjugate of 3  5i ?
a) 5i  3
b) 3  5i
_____ 4. Simplify:
 6  7i 
5.
d) 54  3i
c) i
d) –i
c) 5  3i
d) 3  5i
2
a) 36  49i 2
b) 13  84i
Simplify.
c) 44  45i
c) 85  84i
d) -13
2  5i
6  8i
MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c and
f(x) = a(x – h)2 + k.
_____ 6. The domain of the given function is…
a)
all real numbers
c) x  3
b)
d) x  2
x3
_____ 7. The range of the given function is…
a)
all real numbers
y3
b)
c)
d)
c)
d)
y3
y2
_____ 8. The standard form of the equation y = 2(x-3)2 – 1 is…
a)
b)
2 x2  6 x  2
2 x 2  12 x  17
c)
d)
2 x 2  35
4 x 2  35
_____ 9. The vertex form of the equation y = x2 + 2x + 3 is…..
a) (x - 1)2 + 2
c) (x + 2)2 + 3
b) (x + 1)2 + 2
d) (x - 2)2 + 3
MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c and
f(x) = a(x – h)2 + k.
Solve by taking the square root.
10. 2( x  3)2  6  78
Graph. Identify zeros, intervals of increase, intervals of decrease, vertex
and axis of symmetry.
10
9
8
7
6
5
4
3
2
1
11. y  2( x  3)  1
2
Vertex: _____________
Axis of symmetry: __________
Zeros: ______________
Interval of increase: _______________
Interval of decrease: ________________
-4 -3 -2 -1
-1
-2
-3
-4
12.
1 2 3 4 5 6 7 8 9 10
10
9
8
7
6
5
4
3
2
1
f ( x)  x 2  6 x  5
Vertex: _____________
Axis of symmetry: __________
Zeros: ______________
Interval of increase: _____________
Interval of decrease: ______________
-10
Solve by applying the quadratic formula.
13. x2 – 3x = 8
-8
-6
-4
-2
-1
-2
-3
-4
2
4
MM2A4. Students will solve quadratic equations and inequalities in one variable.
_____ 14. Find the solution(s) to the given function…
a)
(1, -5)
c)
6, -4
b)
(0, -4.8)
d)
4, -6
_____ 15. Describe the nature of the roots of the equation
6 x2  2 x  4  0
a)
b)
1 real root
2 real rational roots
c)
d)
2 real irrational roots
2 imaginary roots
_____ 16. Give the value of the discriminant of the equation 4 x 2  8 x  4
a)
0
b)
-128
c)
1
d)
128
Answer each question showing all work algebraically, graphically,
and/or verbally to indicate understanding.
Solve.
17. 4  x  1  1
18. 5 x 2  6 x  9  0
19. x 2  13  6 x
20. x  x  2  8
2
21. Graph y  2  x  4   1
2
2
1
-2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1 2 3 4 5 6 7 8 9 10
MM2A4. Students will solve quadratic equations and inequalities in one variable.
22. Graph y   x  3  1
2
10
9
8
7
6
5
4
3
2
1
-10
-8
-6
-4
-2
-1
-2
-3
-4
2
4
23. Describe the nature of the roots for the equation you graphed in #22.
a) 1 real root
b) 2 imaginary roots
c) 2 real rational roots
d) 2 real imaginary roots
Find the discriminant and determine if the equation has one real, two real, or two
imaginary roots.
24. x2 - x = -10
discriminant:________
# and type of roots:_____________
25. x2 - 12x + 30 = -6
discriminant:________
# and type of roots:_____________
26. -x2 + 3 = -2x2 + 4x
discriminant:________
# and type of roots:_________