1. [6.5, 6.6] Solve by completing the square

and by using the quadratic formula .

Give all solutions, including complex

number solutions . On the exam, there

will be some problems where you will be

asked to complete the square. On others,

you may be asked to use the quadratic

formula.

a) x^{2} + 2x − 2 = 0

b) 2x^{2} + 5x −4 = 0

c) 2x^{2} − 4x + 3 = 0

d) 4x^{2} − 20x + 25 = 0

2. [6.6] Without solving the equation , determine

if the the solution set consists of

two rational numbers , two real numbers

that are not rational, one real number,

or two complex numbers .

a) 12x^{2} + 3x = 2

b) 2x^{2} − 6x − 56 = 0

c) 4x^{2} + 4x + 1 = 0

d) 5x^{2} + 10x + 6 = 0

3. [6.6] Give the derivation of the quadratic

formula. In other words, start with ax^{2}+

bx + c = 0 and solve.

4. [6.7] Solve the equations.

a)

b) x^{4} − 3x^{2} + 2 = 0

c)

d)

5. [7.1] Match the graphs with the functions .

f(x) = (x + 1)^{2}

g(x) = (x − 1)^{2}

h(x) = x^{2} + 1

k(x) = x^{2} − 1

a)

b)

c)

d)

6. [7.2] Explain in words how the graphs of

y = x^{2} and f(x) = a(x − h)^{2} + k are

related. In particular, point out the role

played by each of the numbers a, h, and

k.

7. [7.2] Identify the vertex and the line of

symmetry for the graphs of the quadratic

functions. Then sketch their graphs.

a) f(x) = 3x^{2} − 12x + 7

b) g(x) = x^{2} + 3x + 1

c) w(x) = 4+2x − x^{2}

8. [7.2] Find the maximum value of the

function f(x) = 3 − 4x − x^{2}. (In other

words, find the largest possible value

for f(x).) Does f(x) have a minimum

value?

9. [7.3] Find the minimum value of the

function f(x) = 1+6x + x^{2}. Does the

function have a maximum value?

10. [7.2] A fence is to be built along the side

of a very long barn to create a hog pen.

There is 240 feet of fence avialable to

build three sides of the pen and the barn

will serve as the other side. What should

the dimensions of the pen be in order to

make the pen as large as possible?

11. [8.1] Find the domain of the functions.

12. [8.1] Reduce the rational functions to

lowest terms .

13. [8.1] Explain why the functions f(x) =

and
are not the

exact same functions.

14. [8.2] Multiply or divide the rational functions

and simplify the answer .

15. [8.3] Add or subtract the rational functions

as indicated. Simplify your answer.

16. [8.3] Compute and simplify.