Extra Explore Math Exploration

OPTIONAL exploration

This exploration could possibly be used as an artifact for your portfolio.

1. Explore the general form of a quadratic equation y=ax^2+bx+c using the ExploreMath Shockwaveinternet activity at
http://exploremath.com/activities/Activity_page.cfm?ActivityID=13

Click on the option to view the vertex trail. Then use the sliders to determine how the coefficients a, b, and c affect the graph of the function.

In general, what do changes in a change about the graph? b? c?
How does each coefficient affect the location of the vertex?

2. Compare and contrast, including screenshots where appropriate, the effect of the coefficients in both the general (y=ax^2+bx+c) and transformational form (y=a(x-h)^2 +k) of a quadratic equation.
Things to think about:

How did your experience with this assignment affect your own understanding of quadratic functions?
What are some of the implications for teaching and learning quadratic functions when using technology and having students focus on relationships between the algebraic equation and graphical representations?

For the SERIOUS & CURIOUS: Considering your exploration above with the ExploreMath activity, derive three different equations (in terms of a, b, and c) that describe the path of the vertex (use the vertex trail option on the ExploreMath website) when a changes, when b changes, and when c changes in the general form of a quadratic function. Show all work and explain how you discovered these equations.