Quadratic Functions

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Quadratic Functions The Discriminant

• Created by Patricia Snow

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Examples of real life parabolas created by
quadratic equations
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Objective

• This presentation was designed for an Algebra II
  class targeting student in the 10-12th grades.
• This is a review of Solving Quadratic Equations,
  using factoring, completing the square and the
  Quadratic formula.
• It is also a review of the Discriminant and what
  information it reveals.

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What is a Quadratic Function?

An Equation of the form AX2BXC0 Where A,BC
are constants, A?0, And X is a variable.
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Techniques used to solve them!
By factoring
Completing the square
Quadratic Formula
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Quadratic Formula
X
-B v(B2-4AC) 2A
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Discriminant

• B2-4AC

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What does the Discriminant mean?

• B2-4AClt 0, the are no real roots.
• B2-4ACgt0, the are two unequal roots.
• B2-4AC0, there is exactly one real root.

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What does this mean graphically?
B2-4AClt0, no real roots
B2-4AC0, one real root
B2-4ACgt0, two unequal root
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TEKS OBJECTIVE

• 3. The student formulates equations and
  inequalities based on quadratic functions, uses a
  variety of methods to solve them, and analyzes
  the solutions in terms of the situation.
  Following are performance descriptions.
• b. The student analyzes and interprets the
  solutions of quadratic equations using
  discriminants and solves quadratic equations
  using the quadratic formula

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Credits

• Sullivan, Michael. Algebra Trigonometry
  (fifth ed.). Prentice Hall Upper Saddle River,
  NJ, 1999. p.113-116
• Sallas, Hille, Etgen, eds. Calculus one and
  several variables(eighth edition). John Whiley
  Sons,inc New York 1999.
• clip art reminder from teacherfiles.com
  http//www.teacherfiles.com/clip_general.htm
• All other clip art from inspiration 6