Algebra 2 - Quadratic Equations Flashcards
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Questions and Answers

What is the standard form of a quadratic equation?

y = ax² + bx + c

What are the factors of the number 12?

  • 1, 2, 3, 4, 6, 12 (correct)
  • 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12 (correct)
  • 2, 3, 6
  • 1, 4, 7, 12

    • What is the Quadratic Function?

    f(x) = x²

    What is a parabola?

    <p>A curved graph of a quadratic function.</p> Signup and view all the answers

    What are some real world examples of quadratic parabolas?

    <p>The Saint Louis Arch, The Golden Arches of McDonald's, The base of Eiffel Tower</p> Signup and view all the answers

    What is a vertex?

    <p>The turning point of the graph of a function.</p> Signup and view all the answers

    What is an axis of symmetry?

    <p>A vertical line that divides the parabola into two congruent halves.</p> Signup and view all the answers

    What is a domain?

    <p>A set of all x values in a function.</p> Signup and view all the answers

    What is a range?

    <p>A set of all y values in a function.</p> Signup and view all the answers

    Is this written in standard form? 3x+x²+12

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

    Is this written in standard form? 6=7x−x²

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

    Is this written in standard form? 4x²+3x+2

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

    Factor the following problem: x²+8x+12

    <p>(x+2)(x+6)</p> Signup and view all the answers

    What is a coefficient?

    <p>The number multiplied by a variable.</p> Signup and view all the answers

    What is a leading coefficient?

    <p>The first number in a line of coefficients and variables.</p> Signup and view all the answers

    What is a monomial?

    <p>An expression with just one term.</p> Signup and view all the answers

    What is a binomial?

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

    What is a trinomial?

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

    What is a polynomial?

    <p>An expression with more than three terms.</p> Signup and view all the answers

    What is the first step when factoring a trinomial?

    <p>Create a binomial skeleton containing the correct signs of the bx and c terms.</p> Signup and view all the answers

    What is the second step when factoring a trinomial?

    <p>Identify factors of the constant.</p> Signup and view all the answers

    What is the third step when factoring a trinomial?

    <p>Drop factors into the skeleton.</p> Signup and view all the answers

    What is the fourth step when factoring a trinomial?

    <p>Check by multiplying both binomials.</p> Signup and view all the answers

    Is the statement x² = x¹*x¹ true or false?

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

    What is the FOIL method?

    <p>Multiplying two binomial answers of a trinomial expression.</p> Signup and view all the answers

    What is the BOX method?

    <p>Multiplying two binomial answers of a trinomial expression using a 2x2 square.</p> Signup and view all the answers

    X² - 4x + 4 is an example of what?

    <p>A perfect square trinomial.</p> Signup and view all the answers

    X² - y² = (x + y)(x - y) is an example of what?

    <p>A difference of two squares.</p> Signup and view all the answers

    Define perfect square trinomials.

    <p>The product you get when you multiply a binomial by itself twice.</p> Signup and view all the answers

    Define difference of two squares.

    <p>Two terms that are squared and separated by a subtraction sign.</p> Signup and view all the answers

    What is the zero product property?

    <p>Set both factors to equal zero and solve.</p> Signup and view all the answers

    Study Notes

    Quadratic Equations

    • Standard form of a quadratic equation: ( y = ax^2 + bx + c ) (e.g., ( x^2 + 8x + 12 ))
    • Non-standard example: ( x - 4 + 3x + x^4 )

    Factoring

    • Factoring involves breaking down numbers or expressions into products of their factors.
    • Example of factors of 12: ( 1, 2, 3, 4, 6, 12 ) and their negative counterparts.

    Quadratic Function

    • A quadratic function is defined as ( f(x) = x^2 ).
    • Example coordinate calculation: For ( x = -2 ), ( f(-2) = 4 ) leading to point (-2, 4).

    Parabola

    • A parabola is the graphical representation of a quadratic function.

    Real-World Applications

    • Examples of quadratic parabolas include the Saint Louis Arch, McDonald's Golden Arches, and the base of the Eiffel Tower.

    Vertex

    • The vertex is the turning point of a parabola, which can be a maximum or minimum.

    Axis of Symmetry

    • The axis of symmetry is a vertical line that divides a parabola into two congruent mirrors.

    Domain and Range

    • Domain: Set of all possible x values for a function.
    • Range: Set of all possible y values for a function.

    Standard Form Validity

    • ( 3x + x^2 + 12 ) is not in standard form; correct form is ( x^2 + 3x + 12 ).
    • ( 6 = 7x - x^2 ) is not in standard form; correct form is ( -x^2 + 7x - 6 ).
    • ( 4x^2 + 3x + 2 ) is in standard form.

    Factoring Example

    • Factoring ( x^2 + 8x + 12 ) yields ( (x + 2)(x + 6) ).

    Coefficients

    • A coefficient is a number multiplied by a variable (e.g., in ( 5x ), 5 is the coefficient).
    • The leading coefficient is the first number in standard form (e.g., ( 7 ) in ( 7x^3 - 2x^2 + 2x - 4 )).

    Types of Expressions

    • Monomial: Expression with one term (e.g., ( 3x^2 )).
    • Binomial: Expression with two terms (e.g., ( 3x^2 + 2 )).
    • Trinomial: Expression with three terms (e.g., ( 3x^2 - 4x + 2 )).
    • Polynomial: Expression with more than three terms (e.g., ( x^4 - 2x^3 + 5x^2 + x - 1 )).

    Steps for Factoring Trinomials

    • First step: Create a binomial skeleton with appropriate signs (e.g., ( + )( + )).
    • Second step: Identify factors of the constant and their sums to match the ( bx ) term.
    • Third step: Insert factors into the skeleton.
    • Fourth step: Verify by multiplying the binomials.

    Exponential Properties

    • Exponential multiplication rule: ( x^2 = x^1 \cdot x^1 ) is true; exponents are added (e.g., ( 5x^2 \cdot x = 5x^3 )).

    Methods for Checking Factorization

    • FOIL method: Used for multiplying two binomials (stands for First, Outer, Inner, Last).
    • BOX method: A visual method using a square to organize terms.

    Special Types of Trinomials

    • Perfect square trinomial: Formed by squaring a binomial (e.g., ( (x - 2)(x - 2) = x^2 - 4x + 4 )).
    • Difference of two squares: Formula ( x^2 - y^2 = (x + y)(x - y) ) (e.g., ( x^2 - 4 = (x + 2)(x - 2) )).

    Zero Product Property

    • When the product of two factors equals zero, set each factor to zero and solve.

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    Test your knowledge of quadratic equations with this set of flashcards. Learn the standard form of a quadratic equation and the process of factoring. Perfect for Algebra 2 students looking to reinforce their understanding.

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