Algebra II SOL Flashcards Overview

Direct Variation

• Represented by the equation y = kx, indicating a linear relationship where y varies directly with x.

Inverse Variation

• Expressed as y = k/x or xy = k, showing that as one variable increases, the other decreases.

Joint Variation

• Defined by the equation y = kxz, indicating that y varies directly with both x and z simultaneously.

Constant of Proportionality

• Denoted by k, it is the constant factor that relates two proportional quantities.

Imaginary Unit (i) Power Properties

• i^2 equals -1, establishing the basis for complex numbers.
• i^3 equals i, continuing the cyclical pattern of powers of i.
• i^4 equals 1, completing the cycle back to one.

Reducing Large Exponents of i

• To simplify large exponents of i, divide the exponent by four:
  • Resulting values:
    • Remainder 0 = 1
    • Remainder 1 = i
    • Remainder 2 = -1
    • Remainder 3 = -i

68-95-99.7 Rule

• Also known as the empirical rule, it indicates that in a normal distribution:
  • Approximately 68% of values lie within one standard deviation of the mean.
  • About 95% within two standard deviations.
  • Roughly 99.7% within three standard deviations.

First Step to Factoring

• The greatest common factor (GCF) should always be identified first to simplify expressions before further factoring.

Graph Types

• Logarithmic graph: y = logx, illustrating the relationship between the logarithm of x and y.
• Absolute value graph: y = |x|, presenting a V-shaped graph showing distance from the origin.
• Exponential graph: y = 2^x, demonstrating exponential growth.
• Square root graph: y = √x, showing a gradual increase starting from the origin.
• Cubic graph: y = x^3, representing a curve that passes through the origin with changing concavity.
• Cube root graph: y = ^3√x, illustrating the gradual increase of y relative to x, including negative values.

General Form of a Line

• The equation y = a(x - h) + k describes a linear function, where:
  • a > 1 indicates a steeper slope (skinny graph).
  • h represents the horizontal shift, affecting where the graph intersects the x-axis.
  • k represents the vertical shift, affecting where the graph intersects the y-axis.