quadratics and imaginary numbers review eq: how do i solve ... · 1/10/2015 · notes quadratic...
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Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:22 PM
Quadratics and Imaginary Numbers Review
EQ: How do I solve a quadratic?
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:22 PM
Operating with Imaginary Numbers
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:22 PM
Simplifying Imaginary Numbers
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:22 PM
Operating with Imaginary Numbers
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:39 PM
Complex Numbers
Always take the form (a + bi)
The real portion comes first, the imaginary second
Complex Conjugate: (a bi)
(2x 3i)(2x + 3i)
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:44 PM
Multiplying and Dividing Complex Numbers
5i(6 3i)
(2 + 4i)(6 9i)
(3 i)(2 + i)
(6 7i)(6 + 7i)
(3 2i)(4 + i)
(6 + 4i)(1 3i)
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 1910:23 PM
Standard form of a Quadratic
ax2 + bx + c = 0
Discriminant: b2 4ac
Discriminant > 0: 2 real rootsDiscriminant = 0: 1 real root
Discriminant < 0: 2 imaginary roots
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:47 PM
Solving a Quadratic
Solve by 1 of 3 ways:a. Factoringb. Completing the Squarec. Quadratic Formula
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:49 PM
Solving a Quadratic by Factoring
1. Set equal to 0.
2. Factor.
3. Set each factor equal to 0 and solve for the variable.
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:49 PM
Examples of Solving by Factoring1. 6x2 = 2x 3. 2x2 + 2x + 15 = 15x
2. 2x2 6x = x2 + 27 4. 5x3 + 6x2 = 9x2 10x
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:49 PM
Solving a Quadratic by Completing the Square
1. Set equal to 0.
2. Factor out a from ax2 + bx to make
3. Move constant to the other side of the equation.
4. Add to each side of the equation to make a perfect square.
5. Factor the perfect square.
6. Squareroot each side and set factor equal to the positive and negative root.
7. Solve for the variable.
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 1910:05 PM
Examples of Solving by Completing the Square
1. x2 8x 12 = 0
2. 2x2 8x + 8 = 4
3. 6x2 + 3 = 11x
4. 3x2 3x = 8
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 1910:11 PM
Solving by Quadratic Formula
1. Set equal to zero.
2. Label a, b, and c by ax2 + bx + c = 0.
3. Plug into the formula and simplify.
Notes Quadratic and Imaginary Numbers Review.notebook
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January 20, 2015
Jan 199:49 PM
Examples of Solving by Quadratic Formula1. 6x2 = 2x
2. x2 8x = 16
3. 4x2 + 6x = 30
4. 2x2 + 2x + 15 = 15x
5. 6x2 = 9x2 10