Advanced Algebra 2 Flashcards

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Questions and Answers

What is standard form?

Ax + By = c

Which of the following are rules of standard form? (Select all that apply)

Reduce (correct)

No fractions (correct)

A must be negative

No decimals (correct)

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?

Y-intercept Signup and view all the answers

How do you find the X and Y intercepts?

Input 0 in the X and Y Signup and view all the answers

What does domain refer to?

X-coordinate Signup and view all the answers

What does range refer to?

Y-coordinate Signup and view all the answers

What is a discrete function?

A function that stops Signup and view all the answers

What is a continuous function?

A function that continues on forever Signup and view all the answers

What is slope represented by?

Y/X Signup and view all the answers

What is the slope formula?

Y2 - Y1 / X2 - X1 Signup and view all the answers

What is the slope-intercept form?

Y = mx + b Signup and view all the answers

What does 'M' represent in an equation?

Slope Signup and view all the answers

What does 'B' represent in an equation?

Y-intercept Signup and view all the answers

Write an equation in slope-intercept form with slope and y-intercept.

Y = mx + b Signup and view all the answers

What is the relationship between perpendicular lines and x-intercept?

Opposite reciprocal Signup and view all the answers

What is the formula for a line parallel to a given line that passes through two points?

Y2 - Y1 / X2 - X1 Signup and view all the answers

What is point-slope form?

Y - Y1 = m(X - X1) Signup and view all the answers

What are the points (1,1), (-1,1), (2,4), and (-2,4) associated with?

Quadratic Signup and view all the answers

What does |X| + 1 indicate on a graph?

Up 1 Signup and view all the answers

What does |X| - 2 indicate on a graph?

Down 2 Signup and view all the answers

What does Y = x² - 4 indicate?

Down 4 Signup and view all the answers

What does Y = x² + 3 indicate?

Up 3 Signup and view all the answers

What does |x + 1| indicate on a graph?

Left 1 Signup and view all the answers

What does |x - 2| indicate on a graph?

Right 2 Signup and view all the answers

What does (X + 3)³ indicate on a graph?

Left 3 Signup and view all the answers

What does (X - 4)² indicate on a graph?

Right 4 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

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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.