Algebra 1 Flashcards: Roots and Solutions
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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?

    <p>The number X is raised to.</p> Signup and view all the answers

    What is the Y-intercept?

    <p>When X is equal to 0.</p> Signup and view all the answers

    What is the X-intercept?

    <p>When Y is equal to 0.</p> Signup and view all the answers

    What does slope represent?

    <p>'Rise over Run'.</p> Signup and view all the answers

    What is a linear equation?

    <p>When X is the highest degree in an equation.</p> Signup and view all the answers

    What is a quadratic equation?

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

    What is slope-intercept form?

    <p>y=mx+b.</p> Signup and view all the answers

    What is standard form?

    <p>4x-3y+5.</p> Signup and view all the answers

    What are translations of a graph?

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

    How does a graph translate up or down?

    <p>By adding or subtracting to move up or down.</p> Signup and view all the answers

    How does a graph translate left or right?

    <p>By adding or subtracting inside parentheses.</p> Signup and view all the answers

    What is the reflection over the Y-axis?

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

    What is the reflection over the X-axis?

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

    What does a parabola represent?

    <p>Name of the curve for x-squared.</p> Signup and view all the answers

    What indicates a quadratic graph facing downward?

    <p>When X^2 is negative.</p> Signup and view all the answers

    What indicates a quadratic graph facing upward?

    <p>When X^2 is positive.</p> Signup and view all the answers

    What is a binomial?

    <p>An expression with 2 terms.</p> Signup and view all the answers

    What is a trinomial?

    <p>An expression with 3 terms.</p> Signup and view all the answers

    What does FOIL stand for?

    <p>First, Outer, Inner, Last.</p> Signup and view all the answers

    What does combining like terms involve?

    <p>Adding terms together with the same degree.</p> Signup and view all the answers

    Are negative numbers any number less than 0?

    <p>True</p> Signup and view all the answers

    Are positive numbers any number greater than 0?

    <p>True</p> Signup and view all the answers

    What is the quadratic formula?

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

    What does the axis of symmetry represent?

    <p>Divides a quadratic graph in half.</p> Signup and view all the answers

    What is the vertex of a quadratic graph?

    <p>Furthest most point of a quadratic graph.</p> Signup and view all the answers

    What is the domain in a function?

    <p>The places where all the Xs are or will go.</p> Signup and view all the answers

    What is the range in a function?

    <p>Places where all the Ys are or will go.</p> 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.

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    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.

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