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