Podcast
Questions and Answers
What are the roots, solutions, zeroes?
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?
How many roots, solutions, zeroes does a polynomial have?
Look at the highest degree of X.
What does X^2 represent?
What does X^2 represent?
The carrot means something is being squared.
What is the degree of X?
What is the degree of X?
What is the Y-intercept?
What is the Y-intercept?
What is the X-intercept?
What is the X-intercept?
What does slope represent?
What does slope represent?
What is a linear equation?
What is a linear equation?
What is a quadratic equation?
What is a quadratic equation?
What is slope-intercept form?
What is slope-intercept form?
What is standard form?
What is standard form?
What are translations of a graph?
What are translations of a graph?
How does a graph translate up or down?
How does a graph translate up or down?
How does a graph translate left or right?
How does a graph translate left or right?
What is the reflection over the Y-axis?
What is the reflection over the Y-axis?
What is the reflection over the X-axis?
What is the reflection over the X-axis?
What does a parabola represent?
What does a parabola represent?
What indicates a quadratic graph facing downward?
What indicates a quadratic graph facing downward?
What indicates a quadratic graph facing upward?
What indicates a quadratic graph facing upward?
What is a binomial?
What is a binomial?
What is a trinomial?
What is a trinomial?
What does FOIL stand for?
What does FOIL stand for?
What does combining like terms involve?
What does combining like terms involve?
Are negative numbers any number less than 0?
Are negative numbers any number less than 0?
Are positive numbers any number greater than 0?
Are positive numbers any number greater than 0?
What is the quadratic formula?
What is the quadratic formula?
What does the axis of symmetry represent?
What does the axis of symmetry represent?
What is the vertex of a quadratic graph?
What is the vertex of a quadratic graph?
What is the domain in a function?
What is the domain in a function?
What is the range in a function?
What is the range in a function?
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.