Algebra 1B Review

Linear, Exponential, Quadratic Functions

100

Is this equation linear, exponential, or quadratic: 

y = 3(4^x)?

Exponential

200

What is the graph of a quadratic function?

parabola

300

If f(x) = 5 + 2^x, what is f(0)?

f(0) = 6

400

What is the constant ratio if consecutive y-values are:

4, 12, 36, 108

ratio = 3

500

If the population of a town decreases by 7% each year, what is the decay factor?

b = 0.93

Operations with Polynomials

100

Simplify: (7k²+9)+(6k²-11)

13k² - 2

200

Simplify: (2x - 3)²

4x² - 12x + 9

300

Simplify:

(5y²+3y-6)-(2y²-5y+3)

3y² + 8y - 9

400

Simplify: (2x + 7)(x - 5)

2x² - 3x - 35

500

Simplify:

(3x - 1)(4x² + x - 6)

12x³ - x² - 19x + 6

Factoring Polynomials

100

Factor:  45x²y - 18xy³

9xy(5x - 2y²)

200

Factor:  16x² - 1

(4x - 1)(4x + 1)

300

Factor: x² - 11x + 18

(x - 9)(x - 2)

400

Factor: x³ + 2x² - 8x - 16

(x² - 8)(x + 2)

500

Factor: 3x² - 18x - 21

3(x - 7)(x + 1)

Solving Quadratic Equations

100

Solve:  5x² - 1 = 19

x = 2 or x = -2

200

How many roots does this equation have?

y = 6x² - 7x + 1

2 solutions

300

Solve:

x² + 8x = 9

x = -9 or x = 1

400

What is the Quadratic Formula?

x = -b +/- sqrt (b²-4ac)

      ^{-----------------------------}

2a

500

Solve:  4x² = 2x + 3

x = 1 +/- sqrt(13)

      ___________

      4

Graphs of Quadratic Functions

100

Identify the vertex:

y = -4(x+1)² + 2

(-1, 2)

200

What is the equation for the line of symmetry?

y = 3x² - 12x + 1

x = 2

300

What is the y-intercept?

y = 3(x-2)² - 1

(0, 11)

400

Find the x-intercepts:

y = x² + 4x - 12

(-6, 0) and (2, 0)

500

Find the x-intercepts:

y = -2(x-3)² + 16

(3+2sqrt2, 0) and (3-2sqrt2, 0)