Algebra 2 Review

Linear Equations and Inequalities

100

Solve for x: 

2x + 5 = 15

x=5

200

Solve the inequality:

3x - 7 > 2x + 4.

x>11

300

Write the equation of a line in slope-intercept form that passes through (3, -2) and with a slope of 2

y=2x-4

400

Solve the equation:

4(2x - 1) = 2(3x + 2)

x=4

500

Solve the system of equations:

3x - y =9

2x + y = 6

(0,3) or

x=0

y=3

Quadratic Functions

100

What's the vertex form of a quadratic function?

y=a(x-h)²⁺k

200

Factor the quadratic expression: 

x² + 5x + 6.

(x+3)(x+2)

300

Solve for x: 

x² - 9 = 0

x=3

x=-3

400

Find the axis of symmetry of the parabola:

y = -2x² + 8x - 5

Axis of Symmetry is

x=2

500

Complete the square to find the solutions of: 

x² - 6x + 9 = 0

x=-3

Exponential and Logarithmic Functions

100

What's the common base for natural logarithms?

e

200

Solve for x:

3^2x= 27.

x=3/2

x=1.5

300

Simplify the logarithmic expression:

log₂(4) + log₂(8)

log₂(32)

400

Solve the equation: 

e^2x = 25

x=ln(25)/2

500

Express the logarithmic equation log₅(25) = x in exponential form.

5^x=25

Systems of Equations:

100

Solve the system:

2x + y = 7

x - y = 1

(2,1)

x=2

y=1

200

Solve the system:

2x - y = 8

x + 2y =4

(4,0) or

x=4

y=0

300

Classify the system as consistent independent, consistent dependent, or inconsistent:

3x - 2y = 5

6x - 4y = 10

Consistent Dependent

400

Solve the system using the substitution method:

4x - y = 7

x + 2y = 5

(3,5) or

x=3

y=5

500

Solve the system using the elimination method

2x - 3y = 10

4x - 6y = 20

Consistent Dependent

Polynomial Operations:

100

What's the degree of a polynomial?

The Highest Exponent

200

Perform the operation:

(3x² - 2x + 5) + (x² + 3x - 1).

4x² + x + 4

300

Factor the polynomial:

x³ - 8

(x - 2)(x² + 2x + 4)

400

Divide the polynomials:

(3x³ - 9x² + 6x) / (x - 2)

3x² - 3x

500

Find all the roots (real or complex) of the polynomial equation:

x⁴ - 10x² + 9 = 0

x = -3, -1, 1 , 3