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Algebra II Recipe: Quadratic Formula and the Discriminant
A. Quadratic Formula x =
  1. Determine the values of a, b, c.
  2. Substitute the values into the formula.
  3. Simplify using order of operations
    • Once simplified, for the ±, set up one equation with "+"  and another with "-".
  4. These x-values are the solutions AND are the x-intercepts of the graph.
ExamplesExamples:
2x² + x = 5
x² - x = 5x - 9
B. Discriminant - it's the (b² - 4ac) in the quadratic formula
  1. The value of (b2 - 4ac) tells how many solutions or x-intercepts the quadratic equation will have.
    • If (b² - 4ac) > 0, there are two real solutions or x-intercepts
    • If (b² - 4ac) = 0, there is one real solution or x-intercept.
    • If (b² - 4ac) < 0, there are no real solutions or x-intercepts.
ExamplesExamples:
x² - 6x + 10 = 0
x² - 6x + 9 = 0
x² - 6x + 8 = 0



G Redden

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