Algebra Final Review

Vertex Form

100

Write in vertex form:

y = x² + 16x + 71

y = (x + 8)² + 7

200

Write in vertex form:

y = x²  + 4x

y = (x + 2)²− 4

300

Write in Vertex Form:

6x² + 12x + y + 13 = 0

y = −6(x + 1)² − 7

400

What is the vertex?

y = x² + 10x + 33

{-5,8}

500

What is the vertex?

y = 2x² + 36x + 170

{-9,8}

Systems of Equations

100

Solve the system of equations:

y = −3x + 4 

y = 3x − 2

(1,1)

200

Solve the system of equations:

4x + 2y = 10 

x − y = 13

(6,-7)

300

Solve the system of equations:

7x + 2y = −19 

−x + 2y = 21

(-5,8)

400

System of Equations:

−16 + 20x − 8y = 0 

36 = −18y − 22x

(0,-2)

500

Solve this system of equations:

−4y − 11x = 36 

20 = −10x − 10y

(-4,2)

Factoring

100

Factor:

7x² − 31x − 20

(7x + 4)(x − 5)

200

Factor:

2b² + 17b + 21

(2b + 3)(b + 7)

300

Factor:

5p² − p − 18

(5p + 9)( p − 2)

400

Factor:

7x² − 32x − 60

(7x + 10)(x − 6)

500

Name four values of b which make the expression factorable: 

x² − 3x + b

Answers Vary:

Ex: 0, 2, −4, −10, −18

Explicit/Recursive Equations Equations

100

Write the recursive function:

3,8,13,18,23...

f(1)=3

f(n)=f(n-1)+5

200

Write an explicit function:

11,9,7,5,3...

f(n)=-2(n-1)+11

OR

f(n)=-2n+13

300

Write the explicit function:

2,4,8,16...

f(n)=2ⁿ

OR

f(n)=2(2^n-1)

400

Write a recursive function:

Scott decides to add running to his exercise routine and runs a total of one mile his first week.  He plans to double the number of miles he runs each week.

f(1)=1

f(n)=f(n-1)(2)

500

Write the explicit functions:

Cami invested $6000 into an account that earns 10% interest each year.

f(n)=6000(1.1)ⁿ

Surprise Me!

100

SOLVE:

2m² − 7m − 13 = −10

{ 7 + 73 4 , 7 − 73 4 }

200

Solve:

k² − 31 − 2k = −6 − 3k² − 2k

{ 5/2 , − 5/2}

300

Write in standard form:

y = (x − 2)² − 2

y = x² − 4x + 2

400

Solve for x:

−5(1 − 5x) + 5(−8x − 2) = −4x − 8x

x= -5

500

Solve for a:

24a − 22 = −4(1 − 6a)

No solution