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Intro to Quadratic Equations quiz

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Termini in questo insieme (15)

  • What is the standard form of a quadratic equation?
    The standard form is ax^2 + bx + c = 0, where a, b, and c are constants and the highest power of x is 2.
  • What does it mean when an equation is called a 'second degree polynomial'?
    It means the highest power of the variable in the equation is 2, which is characteristic of quadratic equations.
  • How do you identify the coefficients a, b, and c in the equation 3x^2 + 2x - 6 = 0?
    a is 3, b is 2, and c is -6, corresponding to the coefficients of x^2, x, and the constant term respectively.
  • What is the leading coefficient in a quadratic equation?
    The leading coefficient is the coefficient of the x^2 term, which is 'a' in the standard form.
  • How do you rewrite 5x^2 = x - 3 in standard form?
    Move all terms to one side to get 5x^2 - x + 3 = 0.
  • In the equation 5x^2 - x + 3 = 0, what are the values of a, b, and c?
    a is 5, b is -1, and c is 3.
  • If a quadratic equation is missing the x term, what is the value of b?
    b is 0, since there is no x term present.
  • Can the coefficients a, b, or c in a quadratic equation be fractions or zero?
    Yes, a, b, or c can be fractions, and b or c can be zero as long as the x^2 term is present.
  • Why can't you solve a quadratic equation by simply isolating x like in linear equations?
    Because the x^2 term complicates the equation, and there are often two solutions for x.
  • What is the first step in solving a quadratic equation by factoring?
    Write the equation in standard form with all terms on one side in descending order of power.
  • After factoring a quadratic equation, what do you do next?
    Set each factor equal to zero and solve for x.
  • Why does setting each factor equal to zero work when solving quadratic equations?
    Because if the product of two factors equals zero, at least one of the factors must be zero.
  • What is the 'ac method' used for when factoring quadratic equations?
    The ac method helps find two numbers that multiply to a*c and add to b, which are used to factor the equation.
  • How do you check if your solutions to a quadratic equation are correct?
    Plug the values of x back into the original equation to see if they make the equation true.
  • What are the solutions to x^2 - 9x + 20 = 0 after factoring?
    The solutions are x = 4 and x = 5, found by factoring into (x - 4)(x - 5) = 0.