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Intro to Quadratic Equations quiz #1 Flashcards

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Intro to Quadratic Equations quiz #1
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  • What does it mean for an equation to be 'quadratic in form'?
    An equation is 'quadratic in form' if it can be rewritten as a polynomial of degree 2, typically in the standard form ax^2 + bx + c = 0, where the highest power of the variable is 2.
  • How many solutions can a quadratic equation have?
    A quadratic equation can have up to two solutions.
  • What is the maximum number of solutions a quadratic equation can have?
    The maximum number of solutions a quadratic equation can have is two.
  • What is the leading coefficient in a quadratic equation written in standard form?
    The leading coefficient is the coefficient of the x squared term, represented by 'a' in ax^2 + bx + c = 0. It is the first coefficient in the equation.
  • How do you convert a quadratic equation to standard form if terms are on both sides of the equation?
    Move all terms to one side so the equation equals zero, arranging them in descending order of power. This ensures the equation is in the form ax^2 + bx + c = 0.
  • What value does the coefficient 'b' take if there is no x term in a quadratic equation?
    If there is no x term, the coefficient 'b' is zero. This is equivalent to having a '+ 0x' in the equation.
  • Why can't you solve a quadratic equation by simply isolating x as you do in linear equations?
    Isolating x in a quadratic equation often leads to expressions like the square root of a variable term, which cannot be solved directly. Quadratic equations typically require factoring or other methods to find solutions.
  • What is the purpose of factoring a quadratic equation when solving for x?
    Factoring rewrites the equation as a product of binomials set to zero, allowing you to set each factor equal to zero and solve for x. This method helps find all possible solutions for x.
  • What does the AC method involve when factoring a quadratic equation?
    The AC method involves finding two numbers that multiply to the product of 'a' and 'c' and add up to 'b'. These numbers are then used to split the middle term and factor the equation.
  • How can you verify that a solution to a quadratic equation is correct?
    Substitute the solution for x back into the original equation and check if both sides are equal. If the equation is true, the solution is correct.