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Quadratic Equations & Applications quiz

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이 집합의 용어 (15)

  • What is the standard form of a quadratic equation?
    The standard form is ax^2 + bx + c = 0.
  • What does it mean to solve a quadratic equation?
    It means finding the values of x that make the equation true, or equal to zero.
  • What is the first step when solving a quadratic equation?
    Write the quadratic equation in standard form.
  • How do you factor a quadratic equation like x^2 + 10x + 21 = 0?
    Find two numbers that multiply to 21 and add to 10, which are 3 and 7, so it factors to (x + 3)(x + 7).
  • What property allows you to set each factor equal to zero when solving quadratics?
    The zero product property allows you to set each factor equal to zero.
  • After factoring, what equations do you solve to find the solutions for x?
    Set each factor equal to zero, such as x + 3 = 0 and x + 7 = 0.
  • Why is it important to check your solutions in the original quadratic equation?
    Checking ensures your solutions actually make the equation equal zero and confirms their correctness.
  • How do you express 'the width is four meters less than the length' algebraically?
    Write width as w = l - 4, where l is the length.
  • What equation represents the area of a rectangle in terms of length and width?
    Area = length × width.
  • How do you set up a quadratic equation from a word problem about a rectangle with area 96 and width 4 less than length?
    Set up 96 = l(l - 4), then expand and rearrange to get l^2 - 4l - 96 = 0.
  • When factoring l^2 - 4l - 96 = 0, what two numbers do you look for?
    Look for two numbers that multiply to -96 and add to -4, which are 8 and -12.
  • Why do you reject the negative solution when solving for the length of a rectangle?
    Because a negative length does not make sense in the context of the problem.
  • How do you find the width once you know the length is 12 meters?
    Plug the length into w = l - 4, so width is 12 - 4 = 8 meters.
  • How do you check if your dimensions for the rectangle are correct?
    Multiply the length and width to see if their product equals the given area.
  • What are the main steps for solving quadratic application problems?
    Write the equation in standard form, factor it, set each factor to zero, solve for the variable, and check your answer.