Common Core Algebra Vocabulary Flashcards

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Questions and Answers

What is the absolute value of -3?

3 (correct)

3.5

-3

Define absolute value function.

A function containing |x|, shaped like the letter V.

What does the graph of an absolute value function look like?

V or upside down V.

What does a quadratic graph look like?

Parabola. Signup and view all the answers

What do you know about the slopes of parallel lines?

They are the same. Signup and view all the answers

What do you know about the slopes of perpendicular lines?

They are negative reciprocals. Signup and view all the answers

Axis of symmetry is ALWAYS an equation x = ____.

-b / 2a. Signup and view all the answers

How do you factor the difference of two squares a^2 - b^2?

(a - b)(a + b). Signup and view all the answers

What does it mean 'to factor'?

To break a number or expression down into its multiplicative parts. Signup and view all the answers

What does it mean 'to solve'?

To find the value of a variable that makes an equation true. Signup and view all the answers

What is the Line of Best Fit or Trend Line?

It is the best line that represents the trend of the data. Signup and view all the answers

What is a residual and when is a residual plot good?

Residual = actual - predicted; a plot is good when there's no pattern. Signup and view all the answers

What is the mode in data?

Most frequent number. Signup and view all the answers

What is the mean in data?

It is the average. Signup and view all the answers

What is the median in data?

It is the middle number or average of the two middle numbers. Signup and view all the answers

Explain how to use the calculator for a Box and Whisker plot.

Hit STAT, then Edit values into L1, then CALC for the 5 number summary. Signup and view all the answers

The range of a data set is calculated as Maximum # - Minimum #.

true Signup and view all the answers

What is the equation of a vertical line?

x = a number. Signup and view all the answers

What is the equation of a horizontal line?

y = a number. Signup and view all the answers

What is a product?

The result of multiplication. Signup and view all the answers

What is a sum?

The result of addition. Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b. Signup and view all the answers

What is the vertex form of a quadratic equation?

y=a(x-h)^2 + k. Signup and view all the answers

What is the standard form of a quadratic equation?

y = ax^2 + bx + c. Signup and view all the answers

What is an algebraic solution?

Solve the problem using variables and equations. Signup and view all the answers

What is an expression?

A mathematical statement with variables and constants but no equal sign. Signup and view all the answers

What is an equation?

A mathematical statement with variables and constants which contains an equal sign. Signup and view all the answers

What is the associative property?

Sum or product of terms has the same value regardless of grouping. Signup and view all the answers

What is a base?

A number that is raised to a power. Signup and view all the answers

What is a binomial?

Polynomial with two terms. Signup and view all the answers

What is bivariate data?

Data involving two separate things being measured. Signup and view all the answers

What is a box and whisker plot?

A graphical representation of data distribution. Signup and view all the answers

What is closure in mathematics?

An operation is closed if the output is the same type as the input. Signup and view all the answers

What is a coefficient?

The numerical factor of a term in a polynomial. Signup and view all the answers

What is the greatest common factor (GCF)?

The largest factor that divides two or more numbers. Signup and view all the answers

Study Notes

Absolute Value and Functions

Absolute value represents the distance from zero on a number line, e.g., |-3| = 3 and |5| = 5.
Absolute value functions include the expression |x| and have a "V" shape graph.

Graphs and Shapes

Absolute value function graphs appear as "V" or inverted "V".
Quadratic graphs form a parabola, which can be "U"-shaped with a vertex at the peak or trough.

Lines and Slopes

Parallel lines possess identical slopes.
Perpendicular lines have slopes that are negative reciprocals of one another.

Mathematical Concepts

The axis of symmetry for quadratics is computed using x = -b / 2a.
The difference of two squares factors as (a - b)(a + b).
Factoring involves breaking an expression down into multiplicative components.

Solving Equations

To solve an equation means to determine the variable's value that satisfies it.
The Line of Best Fit or Trend Line best represents data within a scatter plot.

Data Analysis

A residual represents the difference between actual and predicted values, with a good model indicated by a random residual plot.
The mode is the number that appears most frequently in a dataset.
The mean is computed as the average, while the median denotes the middle value of an ordered dataset.

Box and Whisker Plots

For a Box and Whisker plot, enter values into L1 using STAT, then execute 1 Var Stats under the CALC menu to retrieve the five-number summary.

Lines and Equations

Equations for vertical and horizontal lines follow the forms x = constant and y = constant, respectively.
The slope-intercept form is expressed as y = mx + b, where m indicates slope and b represents the y-intercept.

Quadratic Forms

Vertex form of a quadratic: y = a(x - h)^2 + k, where (h, k) is the vertex.
Standard quadratic form: y = ax^2 + bx + c, with 'a' determining the parabola's direction of opening.

Algebra and Expressions

Algebraic solutions utilize variables and equations, with alternatives like guess-and-check earning partial credit.
Expressions are mathematical forms without equal signs, while equations contain them.

Properties and Terms

The associative property states that the grouping of terms does not affect their sum or product.
The base in exponential expressions is the number raised to a power.
A binomial consists of two terms, e.g., (x + 4).

Data Categories

Bivariate data reflects measurements of two distinct variables (e.g., height and age).
A Box and Whisker plot summarizes data distribution.

Closure Property

An operation is closed if it consistently produces outputs of the same type as its inputs, such as positive numbers remaining positive under addition.

Polynomial Terminology

Coefficient refers to the numeric factor of a polynomial term, e.g., in 14x, the coefficient is 14.

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Description

Dive into the essential vocabulary of Common Core Algebra with these flashcards. Each card provides clear definitions and visual representations to help you grasp concepts like absolute value and quadratic graphs. Perfect for students preparing for the Algebra Regents exam.