Algebra 2 CP 11/12 Final Review

Unit 2: Quadratic

100

What is the vertex?

y=3(x-2)²+1

(2,1)

200

How does the graph of y = (x+4)² compare with the graph of the parent function y = x² 

translated 4 units to the left

300

Simplify the expression

(4+i)(5+i)

19+9i

400

Factor completely

9x²-81

9(x-3)(x+3)

500

Solve:  x²+7x-1=0

-7+or - square root of 53 over 2

Unit 3: Polynomial

100

Identify where the zeros are touching or crossing the x-axis.

f(x)=(x+2)(x-4)³(x+1)²

(-2,0) and (-1,0) are crossing

(4,0) is touching

200

Solve:

x⁴-5x²+4=0

x=-1,1,-2,2

300

Factor completely.

5x³-2x²+15x-6

(5x-2)(x²+3)

400

What is the result when (3x³-4x²+6x-1) / (x-5)

3x²+11x+61+304/(x-5)

500

Sketch the graph of the polynomial.

f(x)= -(x-3)(x+5)(x+1)

Sketch

x-intercepts: 3,-5,-1

All crossing

y-intercept: 15

End Behavior: up/down 

Unit 4: Exponential

100

Write the following using radical notation.  Assume that all variables are positive real numbers.

4x^2/5

4 then 5 on foot x under with 2 as exponent

200

Simplify the cube root of 54

3 cube root of 2

300

Simplify

(3x³y)(4xy^-5)

     (5x²)³

12/(125x²y⁴)

400

Solve.

square root(7x-3)=4

x=19/7

500

Simplify

5th root(7x¹⁰y¹¹)

x²y²   5th root(7y)

Unit 5: Logarithm

100

Switch the form

5^x=125

log₅125=x

200

Evaluate  lne⁸=x

x=8

300

What is the inverse of y=ln(x-1)

y^-1=e^x+1

400

Solve  5^3x-1=125^2x+5

x=-16/3

500

Solve  log₃(2x-1)=2

x=5

Unit 6: Rational

100

What could be an extraneous solution for this equation:

y=5/x-6

x=6

200

What is the product 

x(x-3)  _X   (x-1)(x+3)

(x-1)           x(x-3)     

x+3

300

What is the simplified form of

x²-10x-11/x²-1

x-11/x-1

400

Solve

-4   _-   3  ₌   1

x        5      5x

x=-21

500

Sketch the graph

f(x)=5/(x-1)

Sketch

x=1

y=0

(0,-5)