Algebra 2 Vocabulary Flashcards
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Questions and Answers

What is the standard form of a quadratic function?

  • y = a + bi
  • y = mx + b
  • f(x) = a(x - h)^2 + k
  • f(x) = ax^2 + bx + c (correct)
  • What is a parabola?

    A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side.

    What is the vertex form of a quadratic function?

    f(x) = a(x - h)^2 + k

    What is the slope-intercept form of a linear equation?

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

    What defines a quadratic equation?

    <p>An equation of degree 2.</p> Signup and view all the answers

    What is a root of an equation?

    <p>A real number that satisfies the equation.</p> Signup and view all the answers

    What is a zero of an equation?

    <p>An input value that produces an output of zero.</p> Signup and view all the answers

    What is a square root of a number?

    <p>A number y such that y^2 = a.</p> Signup and view all the answers

    What is a complex number?

    <p>A number expressed in the form a + bi.</p> Signup and view all the answers

    What defines an imaginary number?

    <p>A complex number written as a real number multiplied by i.</p> Signup and view all the answers

    What is 'completing the square'?

    <p>A technique used to solve quadratic equations.</p> Signup and view all the answers

    What is the quadratic formula?

    <p>The formula used to solve quadratic equations.</p> Signup and view all the answers

    What is the discriminant in a quadratic equation?

    <p>D = b^2 - 4ac.</p> Signup and view all the answers

    Study Notes

    Standard Form of a Quadratic Function

    • A quadratic function is expressed as f(x) = ax² + bx + c, where a, b, c are real numbers and a ≠ 0.
    • The graph of a quadratic function is called a parabola.

    Parabola

    • A parabola is a symmetrical open plane curve formed by the intersection of a cone and a plane parallel to its side.
    • The trajectory of a projectile under gravity ideally follows a parabolic path.

    Vertex Form

    • The vertex form of a quadratic function is f(x) = a(x - h)² + k, with (h, k) representing the vertex of the parabola.
    • Different textbooks may interpret "standard form" of a quadratic function variably.

    Intercept Form

    • Slope-intercept form is y = mx + b, where m represents the slope and b is the y-intercept.

    Quadratic Equation

    • A quadratic equation is defined as an equation of degree 2, with the highest exponent being 2.
    • The standard form is expressed as y = ax² + bx + c, where a cannot be zero.

    Root of an Equation

    • A real number x is considered a root if it satisfies the equation.
    • Roots correspond to the x-intercepts of the quadratic function, indicating intersection points with the x-axis.

    Zero of an Equation

    • A zero of a function is an input value that results in an output of zero.
    • Zeros are identified as the x-coordinates where the graph intersects the x-axis, also known as x-intercepts.

    Square Root

    • A square root of a number a is a number y such that y² = a.
    • For instance, both 4 and -4 are square roots of 16 since (4)² = (−4)² = 16.

    Complex Numbers

    • A complex number is expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit satisfying i² = -1.
    • In a complex number, a represents the real part, while b denotes the imaginary part.

    Imaginary Numbers

    • Imaginary numbers can be represented as a real number multiplied by the imaginary unit i, defined by i² = -1.
    • For example, 5i is an imaginary number, and its square results in -25.

    Completing the Square

    • Completing the square is a method for solving quadratic equations, graphing quadratic functions, and evaluating integrals.
    • It is particularly useful when factoring does not yield sufficient results or to find irrational and complex roots.

    Quadratic Formula

    • The quadratic formula is utilized to solve quadratic equations and is represented as x = (-b ± √D) / (2a).
    • A quadratic equation typically has two solutions, which are referred to as roots.

    Discriminant

    • The discriminant D = b² - 4ac is calculated from the coefficients of the equation ax² + bx + c = 0.
    • The discriminant indicates the nature and type of roots the quadratic equation possesses.

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    Description

    Test your knowledge of key terms in Algebra 2 with these flashcards. This quiz covers important concepts such as the standard form of a quadratic function and the definition of a parabola. Perfect for students looking to reinforce their understanding of algebra vocabulary.

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