Algebra 1 Flashcards: Roots and Solutions

Questions and Answers

What are the roots, solutions, zeroes?

Factor

Set equal to 0

Solve for X

All of the above (correct)

How many roots, solutions, zeroes does a polynomial have?

Look at the highest degree of X.

What does X^2 represent?

The carrot means something is being squared.

What is the degree of X?

The number X is raised to. Signup and view all the answers

What is the Y-intercept?

When X is equal to 0. Signup and view all the answers

What is the X-intercept?

When Y is equal to 0. Signup and view all the answers

What does slope represent?

'Rise over Run'. Signup and view all the answers

What is a linear equation?

When X is the highest degree in an equation. Signup and view all the answers

What is a quadratic equation?

When X^2 is the highest degree in an equation. Signup and view all the answers

What is slope-intercept form?

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

What is standard form?

4x-3y+5. Signup and view all the answers

What are translations of a graph?

The moving of a graph left or right, and up or down. Signup and view all the answers

How does a graph translate up or down?

By adding or subtracting to move up or down. Signup and view all the answers

How does a graph translate left or right?

By adding or subtracting inside parentheses. Signup and view all the answers

What is the reflection over the Y-axis?

When a point changes from (X, Y) to (-X, Y). Signup and view all the answers

What is the reflection over the X-axis?

When a point changes from (X, Y) to (X, -Y). Signup and view all the answers

What does a parabola represent?

Name of the curve for x-squared. Signup and view all the answers

What indicates a quadratic graph facing downward?

When X^2 is negative. Signup and view all the answers

What indicates a quadratic graph facing upward?

When X^2 is positive. Signup and view all the answers

What is a binomial?

An expression with 2 terms. Signup and view all the answers

What is a trinomial?

An expression with 3 terms. Signup and view all the answers

What does FOIL stand for?

First, Outer, Inner, Last. Signup and view all the answers

What does combining like terms involve?

Adding terms together with the same degree. Signup and view all the answers

Are negative numbers any number less than 0?

True Signup and view all the answers

Are positive numbers any number greater than 0?

True Signup and view all the answers

What is the quadratic formula?

X= [-b (plus or minus) SQUARE ROOT OF (b^2 - 4ac)] all divided by 2a. Signup and view all the answers

What does the axis of symmetry represent?

Divides a quadratic graph in half. Signup and view all the answers

What is the vertex of a quadratic graph?

Furthest most point of a quadratic graph. Signup and view all the answers

What is the domain in a function?

The places where all the Xs are or will go. Signup and view all the answers

What is the range in a function?

Places where all the Ys are or will go. Signup and view all the answers

Study Notes

Roots, Solutions, Zeroes

Defined as the values of X where the equation equals zero.
Found by factoring and setting the equation equal to zero to solve for X.

Number of Roots, Solutions, Zeroes

Determined by the highest degree of X in the equation.
The count matches the number of roots, solutions, or zeroes.

Degree of X

The exponent to which X is raised, e.g., in X^2, the degree is 2.

Intercepts

Y-Intercept: Occurs when X equals 0; also referred to as "b"; it’s where the graph crosses the y-axis.
X-Intercept: Occurs when Y equals 0; it’s where the graph crosses the x-axis.

Slope

Represents the steepness of a line, calculated as "Rise over Run."
Formula for slope: (Y2 - Y1) / (X2 - X1).

Types of Equations

Linear Equation: Highest degree is 1, represented as y = mx + b (e.g., y = 3x + 6).
Quadratic Equation: Highest degree is 2 with terms including X^2 (e.g., y = X^2 + 3X + 7).

Equation Forms

Slope-Intercept Form: Written as y = mx + b, where m is the slope and b is the intercept (e.g., y = 4x - 2).
Standard Form: Represented usually as Ax + By = C (e.g., 4x - 3y + 5).

Graph Translations

Vertical Translations: Achieved by adding/subtracting to the function, e.g., moving 5 units up translates y = X^2 to y = X^2 + 5.
Horizontal Translations: Inside parentheses; moving right subtracts from X, left adds to X (e.g., (X - 4)^2 moves right, (X + 4)^2 moves left).

Reflections

Over Y-Axis: Changes (X, Y) to (-X, Y).
Over X-Axis: Changes (X, Y) to (X, -Y).

Parabola

The graphical representation of a quadratic function, curved upwards or downwards.

Quadratic Graph Direction

Facing Downward: When the coefficient of X^2 is negative.
Facing Upward: When the coefficient of X^2 is positive.

Algebraic Expressions

Binomial: An expression with two terms, e.g., (x - 2).
Trinomial: An expression with three terms, e.g., (X^3 + 5X - 7).

FOIL Method

A technique for multiplying two binomials: First, Outer, Inner, Last; followed by combining like terms (e.g., (x - 3)(x + 6)).

Combining Like Terms

Process of simplifying expressions by adding terms with the same degree (e.g., 5X^2 + 7X - 4X + 10).

Positive and Negative Numbers

Negative Numbers: Less than 0.
Positive Numbers: Greater than 0.

Quadratic Formula

Used when trinomials cannot be factored: X = [-b ± sqrt(b^2 - 4ac)] / (2a).

Axis of Symmetry

Divides a quadratic graph into two mirror images.
Calculated with x = -b/(2a); it's the x-coordinate of the vertex.

Vertex

The highest or lowest point of a quadratic graph, representing max/min.
Located at the x-coordinate of the Axis of Symmetry (-b/2a), with the y-coordinate found by plugging X into the equation.

Domain and Range

Domain: Set of all possible X values (e.g., X ≥ 7).
Range: Set of all possible Y values.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the key concepts of roots, solutions, and zeroes in Algebra 1 with these flashcards. This study aid focuses on understanding how to find and interpret the roots of equations. Perfect for reinforcing your knowledge and preparing for exams.