Download Unit 5A Retake Packet

GPS ALGEBRA
Solving Quadratics
Name __________________________
Solve each quadratic equation by the method/s indicated. Show all work!!! Be neat!
I. Solve x2 – 4 = 0
A. Solve 0 = x2 – 4 using the square root method.
Solutions by square root method____________________
B. Solve 0 = x2 – 4 using the quadratic formula.
Discriminant:_____ Nature of the Root/s:________
Solutions by quadratic formula ________________
C.
Solve x2 – 4 = 0 by factoring.
Solutions by factoring__________________
II. Solve 2x2 + 4x - 6 = 0
A. Solve 0 = 2x2 + 4x - 6 using the quadratic formula.
Discriminant:_____ Nature of the Root/s:________
Solutions by quadratic formula ________________
B. Solve 6 = 2x2 + 4x - 6 by factoring.
Solutions by factoring__________________
III. Solve
-x2
+ 4x - 6 = 0
A. Solve 0 = -x2 + 4x - 6 using the quadratic formula.
Discriminant:_____ Nature of the Root/s:________
Solutions by quadratic formula ________________
IV. Operations with Complex Numbers
A. i121
B. (8 + 5i) + (-3 – 3i)
C. (12 – 6i) – (2 + 7i)
D. (2 + 3i)(4 + 8i)
E.
2  4i
3  8i
GPS ALGEBRA
The Great Quadratic Unit 5A ALMOST THERE
Name:
Period:
MM2N1. Students will represent and operate with complex numbers. (4 points each)
1. (3 points) Which is the value of i 21 ?
2. Find the product: (3  2i)(5  9i) (write answer in standard form)
3. Simplify: (2  5i)2 (write answer in standard form)
4. (3 points) What is the conjugate of 7  6i ?
Simplify by multiplying by the conjugate.
5  2i
5. a)
3  2i
b)
8  3i
2i
Write the following in imaginary form:
6.
 196
7.
 98
Write the expression as a complex number in standard form:
8.
(18  11i )  (14  17i)
9.
7i  (9  i)  6
MM2A4. Students will solve quadratic equations and inequalities in one variable. (5 points each)
10. (4 points) Describe the nature of the roots of the equation by first finding the discriminant:
3x 2  2 x  1  0
a) 1 real root
b) 2 real roots
c) 2 real imaginary roots
d) 2 imaginary roots
11. Give the value of the discriminant of the equation 5 x 2  4 x  1  3x  4
(Hint: put it in standard form first)
12. (4 points) Find the decimal equivalents of the following irrational number. Round your
answers to the nearest hundredth (two decimal places).
12  17
5
13. (4 points) Which of the Quadratic functions below will have the zeros -3i and +3i?
a) x 2  3  0
b) x 2  3  0
c) x 2  9  0
d) x 2  9  0
14. The length of a rectangle is 2x 1 and the width is 3x  4 . The area of the rectangle is 10
square inches. What is the value of x? (Hint: Draw a picture and label the length and width)
a) 2
b) 5
c) 6
d) 7
e) 14
15. An cell phone is dropped from a city building 700 feet tall. Use the function h(t )  16t 2  700 where
h(t) is the height and t is the time in seconds since the phone is dropped. Find the time it takes
before the phone hits the ground (height of the phone is zero). Round your answer to the nearest
hundredth of a second.
Solve by FACTORING when a>1. Show ALL work for credit!!! (leave answers as simplified fractions)
2
16. 12 x  17 x  6  0
17.
20x2 + 3x – 2 = 0
Solve by taking the SQUARE ROOT. Show ALL work for credit!!! (Leave answers as simplified radicals)
18.
2( x  6)2  8  16
19. 2(x – 2)2 = 72
Solve by applying the QUADRATIC FORMULA. Must put in standard form first and fill out the a, b, c
chart! Must show all work for credit! (leave answers as simplified radical!)
20. x2 – 4x – 2 = 0
a=
b=
c=
21. 2x2 + 2 = 3x
a=
b=
c=
22.  x
a=
b=
c=
2
 1  5 x 2  4 x