Algebra 2 Unit 3 Test Flashcards

Questions and Answers

What is the Midpoint Formula?

m = ((x1+x2)/2,(y1+y2)/2)

What is the Distance Formula?

d = √((x1-x2)^2 + (y1-y2)^2)

What is the equation for vertical lines?

x = k

What is the equation for horizontal lines?

y = k Signup and view all the answers

What is the x-intercept?

The point where a line crosses the x-axis, (x, 0) Signup and view all the answers

What is the y-intercept?

The point where a line crosses the y-axis, (0, y) Signup and view all the answers

What is the Standard Form of a line?

Ax + By = C Signup and view all the answers

What is the slope of a line?

Slope = (rise over run) or (y1 - y2) / (x1 - x2) 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 Point-Slope Form of a line?

y - y1 = m(x - x1) Signup and view all the answers

What do parallel lines have in common?

They have the same slope. Signup and view all the answers

What do perpendicular lines do?

They meet at 90 degrees and have opposite reciprocal slopes. Signup and view all the answers

Define 'Relation' in mathematics.

A set of ordered pairs. Signup and view all the answers

What is a 'Function'?

A type of relation where all first components (x) are different. Signup and view all the answers

What is 'Domain' in a function?

All possible first components (x) of a function. Signup and view all the answers

What is 'Range' in a function?

All possible second components (y) of a function. Signup and view all the answers

What is the Difference Quotient?

(f(x + h) - f(x)) / h Signup and view all the answers

What is the equation of a Quadratic Function?

y = x^2 Signup and view all the answers

What is the equation of a Square Root Function?

y = √x Signup and view all the answers

What is the equation of a Cubic Function?

y = x^3 Signup and view all the answers

What is a Nameless Function?

y = (1/x) Signup and view all the answers

What is the equation of an Absolute Value Function?

y = |x| Signup and view all the answers

What is a Vertical Translation?

y = f(x) + c (shift up) or y = f(x) - c (shift down) Signup and view all the answers

What is a Horizontal Translation?

y = f(x + c) (shift left) or y = f(x - c) (shift right) Signup and view all the answers

How do you flip a graph over the x-axis?

y = -f(x) Signup and view all the answers

How do you flip a graph over the y-axis?

y = f(-x) Signup and view all the answers

What happens to a graph when it widens?

y = (fraction < 1)(f(x)) Signup and view all the answers

What happens to a graph when it narrows?

y = (whole number)(f(x)) Signup and view all the answers

What is K - constant variation?

K does not equal 0 Signup and view all the answers

What is Direct Variation?

y = Kx Signup and view all the answers

What is Inverse Variation?

y = (k/x) Signup and view all the answers

What is Joint Variation?

y = Kx^n z^n Signup and view all the answers

What is the Standard Form of the equation of a circle?

(x-h)^2 + (y-k)^2 = r^2, r > 0 Signup and view all the answers

Study Notes

Midpoint and Distance Formulas

Midpoint Formula: m = ((x1 + x2) / 2, (y1 + y2) / 2) calculates the midpoint of two points.
Distance Formula: d = √((x1 - x2)² + (y1 - y2)²) determines the distance between two points in the Cartesian plane.

Line Characteristics

Vertical Line Equation: x = k is the equation representing vertical lines.
Horizontal Line Equation: y = k represents horizontal lines.

Intercepts

X-Intercept: Point where the graph crosses the x-axis, represented as (x, 0). Found by setting y = 0.
Y-Intercept: Point where the graph crosses the y-axis, represented as (0, y). Found by setting x = 0.

Standard Form and Slope Information

Standard Form of a Line: Ax + By = C. To graph, find intercepts by setting variables to zero.
Slope of a Line: Calculated as (rise/run) or (y1 - y2)/(x1 - x2). Vertical lines have an undefined slope, while horizontal lines have a slope of zero.

Line Forms

Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
Point-Slope Form: y - y1 = m(x - x1), using a specific point (x1, y1) on the line.

Line Relationships

Parallel Lines: Have identical slopes and never intersect, denoted as ||.
Perpendicular Lines: Have slopes that are opposite reciprocals and meet at a right angle, denoted as |.

Relations and Functions

Relation: A set of ordered pairs.
Function: A relation where each first component (x) is unique.
Domain: The set of all possible first components (x-values) in a function.
Range: The set of all possible second components (y-values) in a function.

Special Function Types

Quadratic Function: Defined as y = x².
Square Root Function: Denoted as y = √x.
Cubic Function: Represented by y = x³.
Nameless Function: Defined as y = (1/x).
Absolute Value Function: Denoted by y = |x|.

Transformations of Graphs

Vertical Translation:
- y = f(x) + c shifts the graph up by c units.
- y = f(x) - c shifts the graph down by c units.
Horizontal Translation:
- y = f(x + c) shifts left by c units.
- y = f(x - c) shifts right by c units.
Flip Over X-axis: y = -f(x) reflects the graph across the x-axis.
Flip Over Y-axis: y = f(-x) reflects the graph across the y-axis.

Graph Shape Adjustments

Graph Widens: y = (fraction < 1) f(x) increases the width of the graph.
Graph Narrows: y = (whole number) f(x) decreases the width of the graph.

Variations

K-constant Variation: K ≠ 0 indicates a non-zero constant.
Direct Variation: y = Kx shows a direct proportion between y and x.
Inverse Variation: y = (K/x) shows inverse proportionality.
Joint Variation: y = Kx^n z^n incorporates multiple variables raised to powers.

Circle Equation

Standard Form of a Circle: (x - h)² + (y - k)² = r², where (h, k) denotes the center and r is the radius, r > 0.

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Prepare for your Algebra 2 Unit 3 test with these comprehensive flashcards. Each card features essential formulas and concepts, including the Midpoint and Distance formulas, vertical and horizontal lines, and x and y intercepts. Master these topics to excel in your upcoming exam!