2-7 The Quadratic Formula and Completing the Square

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2-7 The Quadratic Formula and Completing the
Square

• The Quadratic Formula

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You probably know the quadratic formula already.

• Here I am going to show you the derivation of the
  quadratic formula. Why here? It comes from
  completing the square. So now that you know
  completing the square you can understand where
  the quadratic formula comes from.
• You dont need to repeat it I just want you to
  follow this process.

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The Quadratic Formula
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The Discriminant

• The quantity is called the
  descriminant. Understanding the value of simply
  the descriminant allows you to evaluate the
  answer you will get.

2 real roots
But what about the graph?
1 rational root
But what about the graph?
2 imaginary roots
But what about the graph?
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Example

• We are going to graph then QF so that you can see
  what the QF actually lets you find.
• Graph then solve
• Graph then solve
• 3. Solve