Review Supplement Unit 4: Solving Quadratic Equations

Review Supplement
4.3-4.4: Solving Quadratic Equations
by Factoring
Unit 4: Solving Quadratic Equations
1.
If
, then what must be
true about and ?
2.
Find the -intercepts of
.
4.
Solve the system of equations by
substitution:
5.
Find the value of .
P. 319-320: 15-24
3.
Find the value of such that
has only one intercept
(3x2)°
4.5: Solve Quadratic Equations by
Finding a Square Root
6.
√
7.
9.
√
10. √
(13x
4)°
√
P. 320: 25-28
On Q6-Q3, simplify each expression
8.
√ √
11.
√
12.
√
√
13.
√
√
√
On Q14-Q15, write a quadratic
equation with the given roots. Write
your answer in the form
.
14.
15.
4.6: Perform Operations with Complex
Numbers
Evaluate each of the following:
16.
20. Find the value of the expression
below and write your answer in
standard form:
P. 318: 2
P. 321: 29-34
17.
18.
19.
21. Expand (
)
22. Write in standard form:
23. Write in standard form:
(
)
(
) (
)
24. Write in standard form:
25. Solve for : (
26. Write a quadratic equation with
the roots
√ . Write
your answer in the form
.
27. Find |
28. Recall that the Mandelbrot Set, M,
is defined by the recursive formula
. In order for the
complex number to be a
member of M, | |
for every
iteration of the formula.
Determine whether
is a
member of M.
29. An quadratic equation is said to be
(
)
in vertex form if
,
where is a scale factor and
(
)is the vertex of the parabola.
Write
in
vertex form.
30. Complete the square on
to derive a
formula to solve for .
|
4.7: Complete the Square
P. 321: 35-37
4.8: Use the Quadratic Formula and
the Discriminant
)
P. 318: 4
P. 321: 38-41
31. Write a quadratic equation with
roots
√
of the form
34. Find the value of so that the
quadratic equation
has number and
type of solutions indicated:
a) 1 real solution
b) 2 real solutions
c) 2 complex solutions
32. Find the value of so that the
quadratic equation
has number
and type of solutions indicated:
a) 1 real solution
b) 2 real solutions
c) 2 complex solutions
35. Solve the quadratic equation
(
)
.
33. Find the value of so that the
quadratic equation
has number
and type of solutions indicated:
a) 1 real solution
b) 2 real solutions
c) 2 complex solutions