Algebra, Exponents, and Coordinate Geometry Review

Vocabulary flashcards covering algebraic rules, linear equations, exponents, radical approximations, and complex numbers based on the lecture transcript.

Slope-Intercept Form

The equation of a straight line written in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Point-Slope Form

The equation of a straight line written as $y - y_1 = m(x - x_1)$, using a given point $(x_1, y_1)$ and slope $m$.

Slope Formula

The ratio representing the steepness of a line given two points, expressed as $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x}$.

Parallel Lines Slope Condition

Two lines in the same plane that never intersect and have equal slopes, defined by $m_1 = m_2$.

Perpendicular Lines Slope Condition

Two lines that intersect at right angles with slopes that are negative reciprocals of each other, defined by $m_1 = -\frac{1}{m_2}$.

Vertical Line Equation and Slope

A vertical line described by $x = c$ (such as $x = 4$), which has an undefined slope represented by m = \frac{\text{#}}{0}.

Horizontal Line Equation and Slope

A horizontal line described by $y = c$ (such as $y = 4$), which has a slope of $m = 0$.

X-intercept

The point where a graph crosses the x-axis, determined by setting $y = 0$ and solving for $x$.

Y-intercept

The point where a graph crosses the y-axis, determined by setting $x = 0$ and solving for $y$.

Quadratic Formula

The standard algebraic formula used to solve quadratic equations, given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Distance Formula

The formula used to measure the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$, defined as $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Approximation of Square Root of 2

The approximate decimal value for the radical expression $\sqrt{2} \approx 1.4$.

Approximation of Square Root of 3

The approximate decimal value for the radical expression $\sqrt{3} \approx 1.7$.

Approximation of Square Root of 5

The approximate decimal value for the radical expression $\sqrt{5} \approx 2.2$.

Imaginary Unit (i)

The fundamental complex unit defined as $i = \sqrt{-1}$, with cyclical power values $i^2 = -1$ and $i^3 = -i$.

Square of a Binomial (Sum)

The algebraic identity for expanding the square of a sum, given by $(x + y)^2 = x^2 + 2xy + y^2$.

Square of a Binomial (Difference)

The algebraic identity for expanding the square of a difference, given by $(x - y)^2 = x^2 - 2xy + y^2$.

Product of Powers Rule

An exponent rule stating that when multiplying powers with the same base, the exponents are added: $x^m \times x^n = x^{m+n}$.

Power of a Power Rule

An exponent rule stating that when raising a power to another power, the exponents are multiplied: $(x^m)^n = x^{mn}$.

Power of a Product Rule

An exponent rule stating that raising a product to an exponent applies that exponent to each base: $(xy)^m = x^m y^m$.

Zero and Undefined Fractions

Arithmetic properties stating that zero divided by any non-zero number equals zero ($\frac{0}{1} = 0$), whereas division by zero is undefined ($\frac{1}{0} = \text{undefined}$).