Podcast
Questions and Answers
What is standard form?
What is standard form?
Ax + By = c
Which of the following are rules of standard form? (Select all that apply)
Which of the following are rules of standard form? (Select all that apply)
What is the place where a line crosses the x-axis called?
What is the place where a line crosses the x-axis called?
X-intercept
What is the place where a line crosses the y-axis called?
What is the place where a line crosses the y-axis called?
Signup and view all the answers
How do you find the X and Y intercepts?
How do you find the X and Y intercepts?
Signup and view all the answers
What does domain refer to?
What does domain refer to?
Signup and view all the answers
What does range refer to?
What does range refer to?
Signup and view all the answers
What is a discrete function?
What is a discrete function?
Signup and view all the answers
What is a continuous function?
What is a continuous function?
Signup and view all the answers
What is slope represented by?
What is slope represented by?
Signup and view all the answers
What is the slope formula?
What is the slope formula?
Signup and view all the answers
What is the slope-intercept form?
What is the slope-intercept form?
Signup and view all the answers
What does 'M' represent in an equation?
What does 'M' represent in an equation?
Signup and view all the answers
What does 'B' represent in an equation?
What does 'B' represent in an equation?
Signup and view all the answers
Write an equation in slope-intercept form with slope and y-intercept.
Write an equation in slope-intercept form with slope and y-intercept.
Signup and view all the answers
What is the relationship between perpendicular lines and x-intercept?
What is the relationship between perpendicular lines and x-intercept?
Signup and view all the answers
What is the formula for a line parallel to a given line that passes through two points?
What is the formula for a line parallel to a given line that passes through two points?
Signup and view all the answers
What is point-slope form?
What is point-slope form?
Signup and view all the answers
What are the points (1,1), (-1,1), (2,4), and (-2,4) associated with?
What are the points (1,1), (-1,1), (2,4), and (-2,4) associated with?
Signup and view all the answers
What does |X| + 1 indicate on a graph?
What does |X| + 1 indicate on a graph?
Signup and view all the answers
What does |X| - 2 indicate on a graph?
What does |X| - 2 indicate on a graph?
Signup and view all the answers
What does Y = x² - 4 indicate?
What does Y = x² - 4 indicate?
Signup and view all the answers
What does Y = x² + 3 indicate?
What does Y = x² + 3 indicate?
Signup and view all the answers
What does |x + 1| indicate on a graph?
What does |x + 1| indicate on a graph?
Signup and view all the answers
What does |x - 2| indicate on a graph?
What does |x - 2| indicate on a graph?
Signup and view all the answers
What does (X + 3)³ indicate on a graph?
What does (X + 3)³ indicate on a graph?
Signup and view all the answers
What does (X - 4)² indicate on a graph?
What does (X - 4)² indicate on a graph?
Signup and view all the answers
Study Notes
Standard Form
- Standard form of a linear equation: Ax + By = c
- Criteria for standard form: no decimals, must be reduced, no fractions, A must be positive
Intercepts
- X-intercept: the point where a line crosses the x-axis
- Y-intercept: the point where a line crosses the y-axis
- To find both intercepts, substitute 0 for X and Y respectively
Guidelines for Functions
- Domain: refers to the x-coordinates of a function
- Range: refers to the y-coordinates of a function
- Discrete function: a function consisting of distinct or separate values, does not continue indefinitely
- Continuous function: a function that continues infinitely without breaks
Slope Concepts
- Slope is defined as the ratio of change in y to change in x (Y/X)
- Slope formula: (Y2 - Y1) / (X2 - X1)
- Slope-intercept form: Y = mx + b, where m represents the slope
- Y-intercept represented by b in the slope-intercept form
Relationship Between Lines
- Perpendicular lines have slopes that are opposite reciprocals of one another
- Parallel lines share the same slope, derived from (Y2 - Y1) / (X2 - X1)
Different Forms of Equations
- Point-slope form of the equation: Y - Y1 = m(X - X1)
- Convert any linear equation into slope-intercept form using Y = mx + b format when provided with the slope and y-intercept
Quadratic Functions
- Key points for a basic quadratic: (1, 1), (-1, 1), (2, 4), (-2, 4)
Transformations of Functions
- Vertical shifts: |X| + 1 shifts the graph up by 1, |X| - 2 shifts the graph down by 2
- Horizontal shifts: |x + 1| shifts the graph left by 1, |x - 2| shifts the graph right by 2
- For quadratic functions: Y = x² - 4 shifts down by 4, and Y = x² + 3 shifts up by 3
- (X + 3)³ and (X - 4)² are transformations indicating left by 3 and right by 4 respectively
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of key concepts in Advanced Algebra 2 with these flashcards. Each card features essential terms and definitions, like standard form, x-intercept, and y-intercept. Perfect for students looking to reinforce their understanding of algebraic fundamentals.
