Solving Quadratic Equations Using the Quadratic Formula

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Solving Quadratic Equations Using the Quadratic
Formula

• MA.912.A.7.2 Solve quadratic equations over the
  real numbers by factoring and by using the
  quadratic formula.

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The Quadratic Formula
The solutions of a quadratic equation written in
Standard Form, ax2 bx c 0, can be found by
Using the Quadratic Formula.
Click on the link below to view a song to help
you memorize it.
http//www.regentsprep.org/Regents/math/algtrig/AT
E3/quadsongs.htm

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Deriving the Quadratic Formula by Completing the
Square.
Divide both sides by a.
Subtract constant from both sides.
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Deriving the Quadratic Formula by Completing the
Square.
Complete The Square
Factor the Perfect Square Trinomial
Simplify expression on the left side by finding
the LCD
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Deriving the Quadratic Formula by Completing the
Square.
Take the square root of both sides
Solve absolute value/ Simplify radical
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Deriving the Quadratic Formula by Completing the
Square.
Isolate x
Simplify
Congratulations! You have derived The Quadratic
Formula
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1 Solve using the quadratic formula.
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Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

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1 Solve by factoring
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2 Solve by factoring
This quadratic is Prime (will not factor), The
Quadratic Formula must be used!
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2 Solve using the quadratic formula.
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Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

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3 Solve using the quadratic formula
The is not a real number, therefore this
equation has NO Real Solution
14
Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

15
4 Solve using the quadratic formula
Would factoring work to solve this equation?
16
Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

17
5 Solve using the quadratic formula.
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5 What if we move everything to the right side?
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Graph

• Clink on link for graphing calculator.
• http//my.hrw.com/math06_07/nsmedia/tools/Graph_Ca
  lculator/graphCalc.html

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The Discriminant
The expression inside the radical in the
quadratic formula is called the Discriminant.
The discriminant can be used to determine the
number of solutions that a quadratic has.
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Understanding the discriminant
Discriminant
of real solutions
Perfect square
2 real rational solutions
Not Perfect
2 real irrational solutions
1 real rational solution
No real solution
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6 Find the discriminant and describe the
solutions to the equations.
2 Real Rational Solutions
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7 Find the discriminant and describe the
solutions to the equations.
No Real Solutions
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8 Find the discriminant and describe the
solutions to the equations.
2 Real Irrational Solutions
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9 Find the discriminant and describe the
solutions to the equations.
1 Real Rational Solution