College Algebra

Polynomial Equations

100

x² - 5x - 24 = 0

x = 8, -3

200

x² - 10x = -3x

x = -5, 2

300

8x² - 6x - 5 = 0

x = 5/4, -1/2

400

x/36 = 25/x

x = 30, -30

500

x² + 21 = -10x

x = -7, -3

Transformations

100

f(x) = ( x + 2)² - 3

Vertical: Down 3

Horizontal: Left 2

200

t(x) = 4^x+2 + 2

Vertical: Up 2

Horizontal: Left 2

300

p(x) = (x - 5)³ + 2

Vertical: Up 2

Horizontal: Right 5

400

g(x) = |x - 3| - 4

Vertical: Down 4

Horizontal: Right 3

500

h(x) = log₄x

Vertical: None

Horizontal: None

Rational Exponents

100

x^2/3 - 2x^1/3 - 8 = 0

x = 64, -8

200

x^2/3 + 10x^1/3 + 21 = 0

x = -343, -27

300

x^2/5 + 8x^1/5 + 15 = 0

x = -3125, -243

400

5x^2/3 + 24x^1/3 - 5 = 0

x = .008, -125

500

2x^1/3 - 11x^1/3 + 12 = 0

x = 3.375, 64

Difference Quotient

100

f(x) = 3 - 4x

-4

200

f(x) = 3x² + 7x - 5

6x + 3h + 7

300

k(x) = 5 - 2x

-2

400

f(x) = x - x²

-2x - h + 1

500

g(x) = x² - 4

2x + h

Absolute Value Equations

100

2/5|10 - x| = 12

x = -20 OR x = 40

200

|3x - 1| = |2x + 4|

x = 1 OR x = 5

300

-2|3x + 1| = -12

x = 5/3 OR x = -7/3

400

6 + |3x - 5| = 6

x = 5/3

500

-6 - 2|3x - 2| = 8

no solution