Algebra II Final

Slope Intercept Form

of an equation of a line is y= mx + b, where m is the slope and b is the intercept.

Point Slope Form

y-y₁ = m(x-x₁) where (x₁,y₁) is a given point on a non vertical line and m is the slope of the line.

Parallel

if and only if they have the same slope.

Perpendicular Lines

if and only if the product of the slope is -1

Bivariate Data

data consisting of pairs of values

Scatter plot

a set of data graphed as ordered pairs in a coordinate plane.

Dot plot

two sets of data plotted as rodered pairs in a coordinate plane.

Positive Corrleation

when the values in a scatter plot are closely linked positively.

Negative correlation

when the values in a scatter plot are closely linked in a negative correlation.

Line of fit

a line that closely approximates a set of data.

Prediction equation

an equation suggested by the points of a scatter plot to predict other points.

Regression line

line of best fit

Correlation coefficient

a measure that shows how well data are modeled by a linear equation.

Very weak

0.01 - 0.20

Weak

0.21 - 0.40

Moderate

0.41 - 0.60

Strong

0.61 - 0.80

Very Strong

0.80 - 0.99

Piecewise-defined function

a function that is written using two or more expressions.

Piecewise-linear function

contains a single expression.

Step function

consists of line segments.

Greatest integer function

written as f(x) = [[x]], is a step function.

Absolute value function

a function written as f(x) = |x|, where f(x) = x if x > 0, 0 if x = 0 for -x if x < 0.

Family of Graphs

is a group of graphs that display one or more similar characteristics.

Parent Graph (Parent Function)

is the simplest form of the graph in the family.

Translation

Moves a figure up, down, left, right.

Dialtion

stretches or compresses the graph.

Reflection

flipping over the x-axis or the y-axis.

Linear Inequality

is a mathematical statement that compares two linear expressions using inequality symbols.

Boundary

a line or curve that separates the coordinate plane into two regions.

The break-even point

is the point at which x = y.

Systems of equations

two or more equations with the same variables.

Constant

when the system of equations has at least one solution.

Inconsistent

when the system of equations has no solution.

Dependent

when the system has exactly one solution.

Independent

when the system has exactly one solution.

Substitution method

a method used to solve a system of equations in which one equation is solved for one variable in terms of the other.

Elimination method

eliminate one of the variables in a system of equations by adding or subtracting the equation.

Consistent Independent, one solution, intersect at 1 point

Identify whether it is inconsistent, consistent independent, or consistent dependent

Inconsistent, no solution, parallel lines

Identify whether it is inconsistent, consistent independent, or consistent dependent

Consistent dependent, infinite solutions, same line

Identify whether it is inconsistent, consistent independent, or consistent dependent

System of Inequalities

a set of inequalities with the same variables. It means finding the ordered pairs that satisfy all of the inequalites in the system.

Positive number

are those which are greater than 0 (>0)

Negative numbers

are those that are less than zero (<0)

Quadratic function

function described by the equation f(x) = ax² + bx + c, ax² is the _________________.

Linear term

in the equation f(x) = ax² + by + c, by is the __________________.

Constant term

in the equation f(x) = ax² + bx + c, c is the constant term.

Parabola

the graph of a quadratic function. The set of all points in a plane that are the same distance from a given point is called the focus and a given line is called the vertex.

Axis of symmetry

a line about which a figure is symmetric.

Vertex

the point at which the axis of symmetry intersects a parabola.

Maximum value

the y-coordinate of the vertex of the quadratic function f(x) = ax² + bx + c, where n < 0.

Minimum value

the y-coordinate of the vertex of the quadratic function f(x) = ax² + bx + c where n > 0

Quadratic Equation

are quadratic functions that are set equation to a value.

Standard Form

ax² + bx + c = 0, where a is not equal to zero and a, b, and c are integers.

Roots

the solutions of a quadratic equation that crosses the x-axis by how many times, the point where the parabola crosses the x-axis.

Zeros

of a function are the x-intercepts of its graph.

Foil Factors

distribute properly to multiply binomials.

Imaginary unit

defined by i²= -1. The number i is the principal square root of -1 that is i = √-1

Pure imaginary numbers

the square roots of negative real numbers.

Complex numbers

are any numbers that can be written in the form of bi, where a and b are real numbers, and i is the imaginary unit. a is called the real part, and b is called the imaginary part.

Complex conjugates

are two complex numbers of a + bi and a - bi. The product of complex conjecugates is always a real number.