Download Review Unit Test- Quadratics 1

Algebra 2H
Review- Test Quadratics #1
Name:____________________________________
Date:_____________________________________
Objective:
To prepare for a test on the following topics:
Quadratics
1.
Graphing Quadratics by finding intercepts, axis of symmetry, and vertex.
2.
Solving for the roots/zeroes
a.
Zero product
b.
Completing the square
c.
Quadratic formula
3.
Standard form (vertex form) equation
4.
Determining the nature of quadratic roots
5.
Determining quadratic equations given the roots
6.
Finding the sum and product of roots
7.
Deriving quadratic formula, sum of the roots, and/or product of the roots
8.
Operations with complex numbers
Mixed Problem Set
1.
Graph the equation f ( x)
x2
3 x 2 by finding the intercepts, axis of symmetry, and vertex.
y
x
2a.
Solve by factoring:
i.
x2
iv.
2x 2
0
ii.
x2
3x 1 0
v.
x 2 100
64
6 x 16
0
0
iii.
x2
3x
40
vi.
x2
6x
0
1
2b.
Solve by completing the square.
i.
x2
3x 2
iv.
x2
9
2c.
Verify all answers in #2b by using the quadratic formula.
i.
x2
3x 2
iv.
x2
9
3.
Put each in standard (vertex) form by completing the square
0
v.
0
0
ii.
0
ii.
v.
4x 2
x2
8x
1
iii.
x2
6 x 10
0
vi.
1 2
x
2
4x 2
x2
8x
1
iii.
x2
6 x 10
0
vi.
1 2
x
2
8x
0
1
x 3
2
8x
0
0
1
x 3
2
0
2
a.
x2
3x 2
d.
x2
9
4.
Describe the nature of the roots of the following:
a.
x2
5.
Write the equation of the quadratic given the roots:
a.
1, 0
0
e.
0
6 x 10
b.
4x 2
x2
8x
1
c.
x2
6 x 10
0
f.
1 2
x
2
0
b.
1 2
x
2
1
x 3
2
b.
2 + i, 2 – i
8x
0
1
x 3
2
0
0
3
6.
Find the sum and product of the roots for each of the following:
a.
x2
7.
Derive the Quadratic Formula and the Sum and Product of Roots formulas.
3x 2
0
b.
4x 2
8x
1
x2
c.
8x
0
8.
Complex Numbers
1. For the complex number 10 4i , identify the real number and the imaginary number.
2. Write the conjugate of each. Then plot all eight complex numbers in the same complex plane.
A) 2 4i
B) 7i
C) 5
D) 3 2i
3. Evaluate.
a) i 6
b) i11
c) i 24
4. Write the expression as a complex number in standard form.
3 2i
a) 5 2i
b) i 7 5i 3 2 3i
d)
2 4i
3 9i
e) 5 2i
2 3 i
c)
2 4i
3 9i
f) 3i 6 5i
4
g) i 2 i
j) 3 2i
h) 2 3i 1 4i
2
i)
3 7i 1 2i
k) 2i 1 4i 1 i
5. Write the expression as a complex number in standard form.
3 3i
2 4i
5
a)
b)
c)
4i
7i
1 i
6. Find the absolute value of the complex number.
a) 2 5i
b) 4 5i
c) 1 5i
d)
8 7i
3 4i
d) 2 i
e)
4 4i
2 9i
e) 5i
5