Chapter 11

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11.1

Videos on the Square Root Property of Equations show how you can use that property to solve quadratic equations.  The videos have several examples.

11V1: Square Root Property of Equations 1

http://www.youtube.com/watch?v=6QTNwvnIoDk

11V2: Square Root Property of Equations 2

http://www.youtube.com/watch?v=lpscRx-Mfdk

11V3: Square Root Property of Equations 3

http://www.youtube.com/watch?v=CTdk7UR9L54

Videos on the Completing the Square show how you can use that property with the Square Root Property of Equations to solve quadratic equations.  The videos have several examples.

11V4: Completing the Square 1

http://www.youtube.com/watch?v=aOS6OfB5-9o

11V5: Completing the Square 2

http://www.youtube.com/watch?v=jP43EY-S_tg

11V6: Completing the Square 3

http://www.youtube.com/watch?v=Ur3mFyTKqQg

11V7: Completing the Square 4

http://www.youtube.com/watch?v=lgWa6CvJjYw

11V8: Completing the Square 5

http://www.youtube.com/watch?v=kx8t-jR_3ZY

OPTIONAL IF YOU NEED HELP WITH WORD PROBLEMS:

Click the link below for a review how to set up and do word problems that involve writing quadratic equations and solving by factoring.  

These may help you in sections 11.1 and 11.2.

11.2

11V9: Completing the Square 6 and Deriving the Quadratic Formula

In this video, we complete the square on a general quadratic equation in standard form to derive the quadratic formula, and learn a song sung to Pop goes the Weasel to help remember the Quadratic Formula.

http://www.youtube.com/watch?v=SCfHulybCH8

11V10: Example Solving a Quadratic Equation by Completing the Square and by using the Quadratic Formula

http://www.youtube.com/watch?v=O4ndRAX5hmc

Videos on the Quadratic Formula show how to use the formula to solve quadratic equations.

11V11: Quadratic Formula 1

http://www.youtube.com/watch?v=LkmjnxZ-FuU

11V12: Quadratic Formula 2

http://www.youtube.com/watch?v=5ONAXvUFMgo

11V13: Quadratic Formula 3

http://www.youtube.com/watch?v=mC3UptAwj8U

11V14: Quadratic Formula 4

http://www.youtube.com/watch?v=p1o3I9nALGY

11V15: Quadratic Formula 5

http://www.youtube.com/watch?v=2RybRJ3aKJY

11V16: The Discriminant: This video defines the discriminant and shows how it is used to determine the kinds of solutions a quadratic equation has, without solving for the actual solutions.

http://www.youtube.com/watch?v=QOqA8KQMJhE

11V17: Solving a Radical Equation that becomes a Quadratic Equation 1

http://www.youtube.com/watch?v=edLm17B5pnU

11V24: Parabolas Part 1: Graph f(x) = x^2, f(x) = x^2 - 4, f(x) = x^2 + 2, f(x) = x^2 - 6

http://www.youtube.com/watch?v=33CYnBnYsyk

11V25: Parabolas Part 2: Coefficient of x^2 is negative; Graph f(x) = -x^2, Graph f(x) = -x^2 + 7, Graph f(x) = -x^2 + 4 

http://www.youtube.com/watch?v=WtHgKSv02lM

11V26: Parabolas Part 3: Graph f(x) = x^2, f(x) = (x - 1)^2, f(x) = (x +2)^2, f(x) = (x + 1)^2, 

http://www.youtube.com/watch?v=g_FXRRKg3UM

11V27: Parabolas Part 4: Graph f(x) = -(x + 1)^2, f(x) = (x - 2)^2 - 4, f(x) = -(x - 3)^2 + 6  

http://www.youtube.com/watch?v=HC5DDlEwTJw

11V28: Parabolas Part 5: Graph f(x) = x^2, f(x) = (1/2)x^2, f(x) = -2x^2, f(x) = (-2/3)x^2, f(x) = (1/4)x^2 

http://www.youtube.com/watch?v=TGLjBgxvaFY

11V29: Parabolas Part 6: Graph f(x) = (1/2)(x + 1)^2 - 3, f(x) = -2(x + 3)^2 + 8

http://www.youtube.com/watch?v=Fw8vuktklwE

11V30: Completing the Square to get a parabola in standard form: This video shows how to get a formula for the equation of the line that is the axis of symmetry, and how to find the vertex point by completing the square on a the equation of a parabola in the form y = ax^2 + bx + c. The formula is then used to find the vertex point for y = x^2 - 4x + 5.

http://www.youtube.com/watch?v=w3OSfRSaVeQ

These videos show how you can use a formula to find the vertex point, and then graph.

11V31: Parabolas Part 7: Graph f(x) = -3x^2 + 6x + 4

http://www.youtube.com/watch?v=RkLSWfoYg98

11V32: Parabolas Part 8: Graph f(x) = (1/2)x^2 + 2x + 6

http://www.youtube.com/watch?v=BXkLUY5JxAE

This next one IS OPTIONAL because it doesn't have audio after 2:50. Sorry!!!!  Hopefully you can follow along by watching.

Parabolas Part 9: Graph f(x) = -2x^2 + 6x

http://www.youtube.com/watch?v=17JyZveJsiE

11V33: Parabolas Part 10: Given the equation of a parabola that is a function in different forms, several examples are provided and we state if the parabola goes up or down, the equation of the axis of symmetry, the vertex point, and y-intercept.

http://www.youtube.com/watch?v=9HE1kWHMTEI

11V34: Find max height of ball: http://youtu.be/3PfiCtfmJA8

This video uses the vertex point of a parabola to find the maximum height of ball thrown in the air given its initial speed.

11V35: Find 2 numbers with minimum product: http://youtu.be/Qs_WqhoVBDI

Find 2 numbers whose difference is 6 and whose product is as small as possible. This is done using a quadratic equation and the vertex point.

NOTE: There are several videos on the web made by others.  See Math Resources for ideas.  

Brightstorm.com has a lot of videos, including these on graphing parabolas:

Basics of parabolas:

http://www.brightstorm.com/math/algebra-2/quadratic-equations-and-inequalities/introduction-to-parabolas

Finding Vertex of a parabola (not in standard form) by completing the square:

http://www.brightstorm.com/math/algebra-2/quadratic-equations-and-inequalities/finding-the-vertex-of-a-parabola-by-completing-the...

Finding vertex, x-intercept(s) if any, y-intercepts, domain, and range of a parabola:

http://www.brightstorm.com/math/algebra-2/quadratic-equations-and-inequalities/finding-intercepts-domain-range-and-vertex-of-a-parabola