Questions and Answers
What is standard form?
Ax + By = c
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?
X-intercept
What is the place where a line crosses the y-axis called?
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How do you find the X and Y intercepts?
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What does domain refer to?
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What does range refer to?
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What is a discrete function?
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What is a continuous function?
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What is slope represented by?
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What is the slope formula?
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What is the slope-intercept form?
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What does 'M' represent in an equation?
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What does 'B' represent in an equation?
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Write an equation in slope-intercept form with slope and y-intercept.
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What is the relationship between perpendicular lines and x-intercept?
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What is the formula for a line parallel to a given line that passes through two points?
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What is point-slope form?
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What are the points (1,1), (-1,1), (2,4), and (-2,4) associated with?
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What does |X| + 1 indicate on a graph?
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What does |X| - 2 indicate on a graph?
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What does Y = x² - 4 indicate?
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What does Y = x² + 3 indicate?
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What does |x + 1| indicate on a graph?
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What does |x - 2| indicate on a graph?
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What does (X + 3)³ indicate on a graph?
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What does (X - 4)² indicate on a graph?
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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
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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.
