Algebra II Extra Credit

Chapter I & II

Chapter III

Chapter IV

Chapter V

Chapter VI

Solve the Absolute Value Equation:

l 2x - 1 l = 5

2x - 1 = 5

2x = 6

x = 3

2x - 1 = -5

2x = -4

x = -2

Solve the following however you'd like.

-4y = 36 + 11x

-10x - 10y = 20

-10y = 10x + 20

y = -x - 2

-4(-x - 2) = 36 + 7x

-28 = 7x

-4 = x

-10(-4)-10y = 20

y = 2

(-4,2)

Write the following equation in vertex form.

y = x² + 16x + 71

x = -B/2a = -16/2(1) = -8 = c

f(-8) = 8² + 16(-8) + c

f(-8) = -192 + 71

f(-8) = -121

(-8, -121)

y = (x + 8) - 121

Classify the following polynomial:

7x³ + 15x²

According to it's standard form, degree, and number of terms.

Standard form: 7x³ + 15x²

Degree: Cubic

Terms: Binomial.

Simplify the following radical expression

√16x⁸

l 4x⁴ l = 4x⁴

999

Solve the following Absolute Value Equation:

2 l x + 9 l + 3 = 7

2 l x + 9 l = 4

(split into two)

x + 9 = 2

x = - 7

x + 9 = - 2

x = -11

999

Solve via substitution.

4x - y = 20

-2x - 2y = 10

-2x - 2 (4x - 20) = 10

-10x + 40 = 10

x = 3

4(3) - y = 20

y = 8

(3,8)

999

Factor the following.

81y² - 49

√81y² - √49

(9x + 7) (9x - 7)

999

Expand the following:

(4y² - 5x)³

64y⁶ - 240y⁴x + 300y²x² - 125x³

999

Simplify.

√72x³y² x √10xy³

√720x⁴y⁵

(√144) x (√5) x (√x⁴) x (√y⁵) x (12) x (√5) x (x²) x (y²√y)

9999

Translate into standard form.

m = -4 through (0,-9)

y = -4x - 9

4x + y = -9

9999

Solve via elimination.

-4y - 11x = 36

20 = -10x - 10y

20 = -10(4) - 10y

20 = 40 - 10y

-2 = y

(11x - 4y = 36)5

(-10x - 10y = 20) -2

55x - 20y = 180

20x + 20y = -40

x = -4

9999

Solve by factoring.

x² - 5x + 6 = 0

(x-2) (x-3)

(x - 2) = 0 (x - 3) = 0

x = 2

x = 3

9999

What are the real and/or imaginary solutions to this polynomial expression?

x³ + 2x² + 5x + 10 = 0

x²(x + 2) 5(x + 2)

(x + 2) (x² + 5) = 0

x = -2

x = +- i √5

9999

Simplify.

(3 + 2√5) (2 + 4√5)

6 + 12 √5 + 4√5 + 8√25

6 + 16√5 + 8(5)

6 + 16√5 + 40

46 + 16√5

99999

Convert the following into standard form:

A line parallel to y = 9/5x - 3 through the point (10,15)

m = 9/5

y = 9/5(10) + b

15 = 18 + b

-3 = b

(y = 9/5x - 3) 5

5y = 9x - 3

-9x + 5y = -3

99999

Represent the following system with a matrix:

x - 3y + z = -6

x + 3z = 12

y = -5x +1

x - 3y + z = -6

x + 0y + 3z = 12

5x + 1y + 0z = 1

1 -3 1 l 6

1 0 3 l 12

5 1 0 l 1

99999

What is the quotient?

9 + 12i / 3i

27i + 36i² / 9i²

27i - 36 / -9

... (Simplify)

-3i + 4

99999

The roots of a cubic polynomial are -2 and 4i. Write the polynomial in standard form.

P(x) = (x + 2)(x-41)(x+4i)

P(x) = (x + 2) (x² + 16)

P(x) = x³ + 2x² + 16x +32

99999

Find the solution for...

√(2x - 3) = 8

√(2x-3) = (5)²

2x = 28

x = 14

999999

Describe the following Transformation:

y = -6 (x - 4)² + 8

Up eight units

Right four units.

999999

Solve the system.

-x - y - 3 = 9

z = -3x - 1

x = 5y - z + 23

-x - y - 3(-3x-1) = 9

8x - y = -12

(8x - y = 12)-5

-2x - 5y = 24

-2(-2) - 5y = 24

-5y = 20

y = -4

-40x + 5y = 60

-2x - 5y = 24

x = -2

z = -3(-2) - 1

z = 5

999999

Your school's jazz band is selling CDs as a fundraiser. The total profit, p, depends on the amount x that your band charges for each CD. The equation:

p = -x²m+48 - 300

models the profit of the fundraiser. What is the least amount, in dollars, you can charge for a CD to make a $200 profit?

200 = -x² + 48x - 300

x² - 48x + 300

x² - 48x + 500 = 0

x = 48 +- √((-48)² - 4(1)(500)) / 2 (1)

x = 48 - 17.4 / 2 = 32.7

x = 48 + 17.4 / 2 = 15.3

$15.30.

999999

Expand the following:

(2x - 5y)⁸

256x⁸ - 5120x⁷y + 44800x⁶y² - 22400x⁵y³ + 700,000x⁴y⁴ - 1,400,000x³y⁵ + 1,750,000x²y⁶ - 1,250,000xy⁷ + 390,625y⁸

999999

Let f(x) = 4x + 7 and

g(x) = √(x) + x

Find ( f + g ) and its domain,

(f + g) (x)

= f(x) + g(x)

= (4x + 7) + (√(x) + x)

= 5x + √(x) + 7

Domain: x >= 0